biol_607_midterm
Wendi White
11/1/2020
github: https://github.com/wendi-white/biol607_homework
#libraries
library(rsample)
library(purrr)
library(dplyr)##
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## intersect, setdiff, setequal, unionlibrary(ggplot2)
library(tidyr)
library(modelr)
library(tidyr)
library(dplyr)
library(ggplot2)
library(stats)
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library(bayesplot)## This is bayesplot version 1.7.2## - Online documentation and vignettes at mc-stan.org/bayesplot## - bayesplot theme set to bayesplot::theme_default()## * Does _not_ affect other ggplot2 plots## * See ?bayesplot_theme_set for details on theme settinglibrary(profileModel)
library(AICcmodavg)
library(compare)##
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## dstudent_t, pstudent_t, qstudent_t, rstudent_tlibrary(rsample)
library(boot)
library(modelr)- Sampling your system (10 points) Each of you has a study system your work in and a question of interest. Give an example of one variable that you would sample in order to get a sense of its variation in nature. Describe, in detail, how you would sample for the population of that variable in order to understand its distribution.Questions to consider include, but are not limited to: Just what is your sample versus your population? What would your sampling design be? Why would you design it that particular way? What are potential confounding influences of both sampling technique and sample design that you need to be careful to avoid? What statistical distribution might the variable take, and why?
One variable I would sample is wrack abundance in order to get its variation across time (seasons/years) and elevation. To sample for a population I would want to do sample transects across high, mid and low elevations at the low tide in the marsh and take data during the low tides during peak wrack season (spring) for maybe about 1 week. I’d imagine wanting to observe the back to back low tides despite lighting issues so I could mark and understand true max rack replacement. This would give me an idea about wrack replacement and if it stays consistent over tides (also track how high each tide is). After peak season I would likely sample once every month until winter when snow started to compile and then start sampling again after the winter months and resume heavy sampling during the spring again. Likely the largest impacts of wrack will happen during spring and it will be essential to have accurate measurements of wrack abundance.
When I go out to sample I would use MARINe protocols for my transects. At the start of the experiment I would set up 10 permanent transects grids that are 100m long and travel back from the creek edges. I can use GPS points or permanent markers (PVC) to set the transects. We’d take a measurement at every 0.5m and record if there was wrack (classified as fresh vs old and also wrack species type) or none.
Answering the questions presented after this brief layout: 1. Just what is your sample versus your population? My sample is the ten transects that start from the creek bank but my population is wrack across the entirety of the marsh to look at its distribution.
What would your sampling design be? Sampling across 10 permanent 100m transects. Data points tell us if there is wrack or not. If there is wrack what species is it? What state is it in (fresh vs old)?
Why would you design it that particular way? I’d design it in this way so I could get an overall idea of the distribution of wrack across the marsh. Using fixed plots will also let us look at wrack replacement during peak season/ over different high tides.
What are potential confounding influences of both sampling technique and sample design that you need to be careful to avoid? Nothing, it’s perfect :) Just kidding. When sampling I’d need to be sure that what I define as “fresh” vs “old” is clear. This would take some field observations and a literature dive as I’m newer to this system. Based on my previous experiences, kelp is old when it’s dried out and/or browned.
What statistical distribution might the variable take, and why? I would imagine that we see differences in wrack abundance maybe across tides but almost certainly across seasons due to higher production of algae during the spring. Also, I would imagine that we would see higher wrack deposits in the high intertidal b/c replacement is dependent on the next high tide and if it will be swept back out or not. The amount of time wrack spends in an area also adds to how long it has to decompose/subsidize the local area.
- Data Reshaping and Visualization. Johns Hopkins has been maintaining one of the best Covid-19 timeseries data sets out there. The data on the US can be found “https://github.com/CSSEGISandData/COVID-19/blob/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_US.csv” with information about what is in the data at “https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data”
2a) Access (5 points) Download and read in the data. Can you do this without downloading, but read directly from the archive (+1)
covid_confirmed <- read.csv("https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_US.csv", check.names = F) #load data but take out the X before all the dates
covid_confirmed<- covid_confirmed[,c(6,7,12:298)] #pull just the admin, state and date columns2b) It’s big and wide! (10 Points) The data is, well, huge. It’s also wide, with dates as columns. Write a function that, given a state, will output a time series (long data) of cumulative cases in that state as well as new daily cases. Note, let’s make the date column that emerges a true date object. Let’s say you’ve called it date_col. If you mutate it, mutate(date_col = lubridate::mdy(date_col)), it will be turned into a date object that will have a recognized order. {lubridate} is da bomb, and I’m hoping we have some time to cover it in the future. +5 extra credit for merging it with some other data source to also return cases per 100,000 people.
func_by_state <- function(state){ #when given a state
#pivot our data longer so that we get a date's become read rowwise not as columns
covid_longer <- pivot_longer(covid_confirmed, -c(Province_State, Admin2),
names_to = "date_col",
values_to = "cumulative_cases") %>%
#creating new date col in form of mdy
mutate(date_col = lubridate::mdy(date_col))
#create a new df that calls for a specific state
specific_state <- covid_longer %>%
#add in a daily cases col that takes cum cases-cum cases from day before to give you updated daily
mutate(daily_cases= (cumulative_cases)-(lag(cumulative_cases, k=1)))%>%
#filter by state
filter(Province_State == state) %>%
#summarize with df of state, date, cum cases, and daily cases
summarize(Province_State, date_col, cumulative_cases, daily_cases)
#final df that groups by dates so that each state has one reading per day not one reading per county per day
df <- specific_state %>%
group_by(date_col)%>%
summarize(new_daily_cases=sum(daily_cases),
cumulative_cases= sum(cumulative_cases))%>%
filter(new_daily_cases >= 0)
return(df)
}
mass_df <- func_by_state("Massachusetts") #test for mass## `summarise()` ungrouping output (override with `.groups` argument)alaska_df <- func_by_state("Alaska") #test for alaska## `summarise()` ungrouping output (override with `.groups` argument)2c) Let’s get visual! (10 Points) Great! Make a compelling plot of the time series for Massachusetts! Points for style, class, ease of understanding major trends, etc. Note, 10/10 only for the most killer figures. Don’t phone it in! Also, note what the data from JHU is. Do you want the cumulative, or daily, or what?
coeff <- 50 #set coeff in order for secondary axis to be of right proportion
#call in mass df and filter for only cases >0 (noticed one neg number in data and also the top number in the column is funky b/c it's doing a cum-last cum so produces large neg #)
mass_plot <- ggplot(data=mass_df %>%
filter(new_daily_cases > 0)%>%
filter(cumulative_cases > 0),
mapping = aes(x= date_col)) +
#x is always date but then two y axis with new daily and cumulative
geom_line(aes(y=new_daily_cases, colour="new_daily_cases")) +
geom_line(aes(y=cumulative_cases / coeff, colour="cumulative_cases")) + # divide by coeff so it's proportional to the other y scale
#the continuous y scale needs the sec axis scale to be set by the coeff
scale_y_continuous(
#First axis name
name = "New daily cases" ,
# Add a second axis and specify name
sec.axis = sec_axis(~.*coeff, name="Cumulative cases")) +
#label whole graph
labs(title= "Changes in new daily annd cumulative cases for Massachusetts",
subtitle = "Tracking changes from Jan-Nov 2020",
x= "Time",
y= "New daily cases")+
#remove legend title
theme(legend.title=element_blank())+
#give lines colors
scale_color_manual(values=c("#CC6666", "#9999CC"))+
transition_reveal(date_col) #animate it so it animates by the date
mass_plot
2d) Cool. Now, write a function that will take what you did above, and create a plot for any state - so, I enter Alaska and I get the plot for Alaska! +2 if it can do daily or cumulative cases - or cases per 100,000 if you did that above. +3 EC if you highlight points of interest - but dynamically using the data. Note, you might need to do some funky stuff to make things fit well in the plot for this one. Or, meh.
func_by_state_plot <- function(state, coeff= 50){ #when given a state and coeff (set at 50 which would work for them all)
##pivot our data longer so that we get a date's become read rowwise not as columns
covid_longer <- pivot_longer(covid_confirmed, -c(Province_State, Admin2),
names_to = "date_col",
values_to = "cumulative_cases") %>%
#creating dates column in mdy format
mutate(date_col = lubridate::mdy(date_col))
#create a new df that calls for a specific state
specific_state <- covid_longer %>%
#add in a daily cases col that takes cum cases-cum cases from day before to give you updated daily
mutate(daily_cases= (cumulative_cases)-(lag(cumulative_cases, k=1)))%>%
#filter by state
filter(Province_State == state) %>%
#summarize with df of state, date, cum cases, and daily cases
summarize(Province_State, date_col, cumulative_cases, daily_cases)
#final df that groups by dates so that each state has one reading per day not one reading per county per day
df <- specific_state %>%
group_by(date_col)%>%
summarize(new_daily_cases=sum(daily_cases),
cumulative_cases= sum(cumulative_cases))
#call in df and filter for only cases >0 (noticed one neg number in data and also the top number in the column is funky b/c it's doing a cum-last cum so produces large neg #)
plot <- ggplot(data=df %>%
filter(new_daily_cases > 0)%>%
filter(cumulative_cases > 0),
#x is always date but then two y axis with new daily and cumulative
mapping = aes(x= date_col))+
geom_line(aes(y=new_daily_cases, colour="new_daily_cases"))+
geom_line(aes(y=cumulative_cases / coeff, colour="cumulative_cases"))+ # divide by coeff so it's proportional to the other y scale
#the continuous y scale needs the sec axis scale to be set by the coeff
scale_y_continuous(
#First axis name
name = "New daily cases",
# Add a second axis and name it
sec.axis = sec_axis(~.*coeff, name="Cumulative cases")) +
labs(title= "Changes in new daily cases and cumulative cases over time",
subtitle = state,
x= "Time",
y= "New daily cases")+
#remove legend title
theme(legend.title=element_blank())+
#give lines colors
scale_color_manual(values=c("#CC6666", "#9999CC"))+
transition_reveal(date_col) #animate it
return(plot)
}
func_by_state_plot("Alaska") #try with alaska## `summarise()` ungrouping output (override with `.groups` argument)
- Let’s get philosophical. (10 points) We have discussed multiple inferential frameworks this semester. Frequentist NHST, Likelihood and model comparison, Baysian probabilistic thinking, Assessment of Predictive Ability (which spans frameworks!), and more. We’ve talked about Popper and Lakatos. Put these pieces of the puzzle together and look deep within yourself. What do you feel is the inferential framework that you adopt as a scientist? Why? Include in your answer why you prefer the inferential tools (e.g. confidence intervals, test statistics, out-of-sample prediction, posterior probabilities, etc.) of your chosen worldview and why you do not like the ones of the other one. This includes defining just what those different tools mean, as well as relating them to the things you study. extra credit for citing and discussing outside sources - one point per source/point
Well to be quite honest I was a frequentist before starting this class. I very heavily relied on running an analysis or looking at an analysis in a paper and saying oh the p-value is low, reject the null, cool. In part this was all I had been taught so it was quite mind bottling to start thinking about statistics in a new way. In the past all I was worried about was much of what the pregnant meme stands for (ensuring you don’t have Type I- rejecting the null even though it’s true or Type II error- failing to reject the null). 95% confidence intervals were a safe place to start!
This year will really be my first attempt at developing a project with statistics in mind. One of the first times I had really thought about statistical theory was upon the introduction of Lakatos and Popper. I more strongly identify with Lakatos b/c of his idea that we need research programs to get at an overall hard core theory. When I conceptually think about the impacts of subsidies on food webs, there are so many examples that can conclude different results. Sometimes subsidies are good and sometimes they can be bad. We create a body of literature as a scientific community to define and build upon current standing theories in an attempt to paint a bigger picture.
Moving into the way I analyze problems though, I now think I most heavily reside with looking at likelihood and model comparisons. After showing us how our linear models are used to do the same interpretations as t-tests, it all really came together for me. I had been relying on my (narrow) previous knowledge and I think needed the dots to connect before I could really commit to understanding why we run linear models. It’s because everything just IS a linear model!! And now I can finally get behind reading the different graphs and seeing how well our data behaves. And then furthering this by looking at how well my data says something about my system is even COOLER! I always relied on a p-value to tell me how confident I can be in my data and the analysis it produces. Now being able to look at a ggplot, which, or qqplot and knowing what to take away from it I feel confident in this type of analysis.
I will admit that I’m still trying to get a better grasp on utilizing bayesian statistics. I haven’t ever used real data with bayes statistics and so I’m having a hard time applying it to a question. Once I begin an experiment and can begin to think about the impacts of a prior on my analysis I could see myself starting to change my mindset to work more with this theorem. When we did the problem with the sun I can see how taking our priors into account is crucial. I also think that analyzing credible intervals could be highly beneficial to understand the probability of observing an unobserved parameter.
Overall, I see this class helping me grow in the way I think about statistics (and read other papers!). I can foresee my mindset changing as I learn more and develop my own research.
- Bayes Theorem (10 points) I’ve referenced the following figure a few times. I’d like you to demonstrate your understanding of Bayes Theorem by hand (e.g. calculate it out and show your work - you can do this all in R, I’m not a monster) showing what is the probability of the sun exploding is given that the device said yes. Assume that your prior probability that the sun explodes is p(Sun Explodes) = 0.0001 (I’ll leave it to you to get p(Sun Doesn’t Explode). The rest of the information you need - and some you don’t - is in the cartoon - p(Yes | Explodes), p(Yes | Doesn’t Explode), p(No | Explodes), p(No | Doesn’t Explode).
The frequentist very heavily relies on the probability of rolling a 6 twice in a row. However, this approach isn’t really answering our question b/c that means we can’t make the argument that we know it’s highly unlikely that the sun is ever going to explode. That is the difference between frequentist and bayes statistics b/c with bayes we can take our prior knowledge into account. It changes it from a 2.7% chance the sun explodes given a yes to a 0.3488141% chance the sun will explode. It’s HIGHLY unlikely!
My math: p(sun exploding | detector says yes) = p(detector says yes | sun exploding) * p(sun exploding) / p(detector says yes)
p(e|d) = p(d|e) p(e) / p(d) = 35/36 0.0001/ 0.02787222 = 0.003488141
p(d|e) lik of observing a yes from the machine given our data that the sun exploded. So this lik is 35/36 b/c the machine only lies to us 1/36 times (1/6 x 1/6= prob of rolling two 6’s)
p(e) prob sun will explode– given as 0.0001
p(d) what is the prob that the detector will detect an explosion. Need to look at the option for the machine correct and explode + machine to lie and explode = ((35/36)0.0001) + ((1 - (35/36))(1 - 0.0001)) = 0.02787222
#p(sun exploding | detector says yes) = p(detector says yes | sun exploding) * p(sun exploding) / p(detector says yes)
#p(e|d) = p(d|e) *p(e) / p(d)
# = 35/36 *0.0001/ 0.02787222
# = 0.003488141
#p(d|e) lik of observing a yes from the machine given our data that the sun exploded. So this lik is 35/36 b/c the machine only lies to us 1/36 times (1/6 x 1/6= prob of rolling two 6's)
#p(e) prob sun will explode-- given as 0.0001
#p(d) what is the prob that the detector will detect an explosion. Need to look at the option for the
#machine correct and explode + machine to lie and explode
#= ((35/36)*0.0001) + ((1 - (35/36))*(1 - 0.0001))
#= 0.027872224a Extra Credit (10 Points) Why is this a bad parody of frequentist statistics?
The frequentist compares the probability of the machine lying to a p-value. They say b/c it’s pvalue is <0.05 the sun has exploded. But the p-value is a completely different thing then the probability ratio, which is why it’s a bad parody of frequentist statistics.
- Quailing at the Prospect of Linear Models I’d like us to walk through the three different ‘engines’ that we have learned about to fit linear models. To motivate this, we’ll look at Burness et al.’s 2012 study "Post-hatch heat warms adult beaks: irreversible physiological plasticity in Japanese quail http://rspb.royalsocietypublishing.org/content/280/1767/20131436.short the data for which they have made available at Data Dryad at http://datadryad.org/resource/doi:10.5061/dryad.gs661. We’ll be looking at the morphology data.
setwd("/Users/wendiwhite/Desktop/Ecology/UMass Boston Masters/UMass Masters classes/bio stats 607/data")
morphology <- read.csv("Morphology data.csv") %>% #load in morph data w/out na's
na.omit()
morphology## bird_num Sex age_days exp_temp_C mass_g tarsus_mm culmen_mm depth_mm
## 1 1 5 15 16.09 19.38 7.64 4.23
## 2 2 m 5 15 19.22 20.38 7.49 4.46
## 3 3 f 5 15 17.51 19.04 7.31 3.92
## 4 4 m 5 15 14.36 20.11 7.34 3.85
## 5 5 f 5 15 17.43 21.82 8.24 4.42
## 6 6 m 5 15 15.66 19.83 6.82 3.65
## 7 7 m 5 15 20.00 21.65 7.84 3.94
## 8 8 5 15 16.42 18.19 7.39 3.72
## 9 9 m 5 15 17.40 19.40 7.40 4.50
## 10 10 f 5 15 20.04 20.91 7.81 4.09
## 11 11 f 5 15 16.19 19.97 6.86 4.61
## 12 12 m 5 15 16.20 18.59 7.83 4.61
## 13 13 f 5 15 17.10 18.67 6.85 4.97
## 14 14 f 5 15 15.62 20.64 6.60 4.15
## 15 15 m 5 15 14.94 18.23 6.47 5.11
## 16 16 f 5 15 23.44 21.59 8.66 4.43
## 17 17 f 5 15 17.31 20.24 7.43 4.31
## 18 18 m 5 15 12.51 17.66 6.84 4.34
## 19 19 f 5 15 15.82 20.36 7.39 4.63
## 20 20 m 5 15 16.47 18.00 8.12 4.21
## 21 21 m 5 30 17.32 19.58 7.21 3.85
## 22 22 f 5 30 20.77 22.34 8.74 4.08
## 23 23 m 5 30 15.53 18.52 6.70 3.98
## 24 24 m 5 30 14.78 19.22 6.66 4.50
## 25 25 m 5 30 15.41 20.23 8.46 4.99
## 26 26 m 5 30 13.56 19.18 6.98 4.92
## 27 27 f 5 30 13.46 17.93 6.86 4.23
## 28 28 f 5 30 17.13 20.74 7.01 3.30
## 29 29 f 5 30 17.29 21.98 9.00 4.19
## 30 30 f 5 30 12.96 18.69 7.36 4.10
## 31 31 f 5 30 17.72 20.47 7.76 4.78
## 32 32 m 5 30 13.72 20.03 6.93 3.32
## 33 33 m 5 30 16.44 19.70 7.91 4.59
## 34 34 m 5 30 16.34 19.59 7.67 4.41
## 35 35 f 5 30 16.22 19.65 7.22 4.76
## 36 36 f 5 30 15.56 19.82 7.26 4.80
## 37 37 5 30 14.48 20.92 7.87 4.35
## 38 38 m 5 30 17.83 19.27 6.64 4.48
## 39 39 f 5 30 15.09 19.39 7.06 4.81
## 40 40 5 30 12.94 19.02 6.60 3.93
## 41 1 7 15 13.84 18.52 7.88 3.54
## 42 2 m 7 15 23.15 19.89 7.95 5.85
## 43 3 f 7 15 21.68 20.63 7.75 4.48
## 44 4 m 7 15 17.44 19.92 6.82 4.46
## 45 5 f 7 15 19.89 19.22 7.55 4.16
## 46 6 m 7 15 17.54 19.42 4.23 4.66
## 47 7 m 7 15 26.82 23.24 8.44 5.48
## 48 8 7 15 18.33 18.76 7.49 5.55
## 49 9 m 7 15 21.39 21.25 7.80 4.30
## 50 10 f 7 15 23.99 20.22 8.50 4.61
## 51 11 f 7 15 18.36 19.06 8.00 3.90
## 52 12 m 7 15 23.32 22.59 8.51 5.40
## 53 13 f 7 15 19.38 20.44 7.49 4.32
## 54 14 f 7 15 16.93 16.19 8.73 4.99
## 55 15 m 7 15 13.76 18.78 6.78 5.60
## 56 16 f 7 15 29.45 23.39 8.82 4.22
## 57 17 f 7 15 20.80 22.31 7.47 4.75
## 58 18 m 7 15 13.67 18.22 6.68 6.92
## 59 19 f 7 15 19.21 21.74 7.38 4.71
## 60 20 m 7 15 18.40 19.91 7.38 4.09
## 61 21 m 7 30 21.38 19.69 7.18 4.27
## 62 22 f 7 30 27.04 22.59 7.91 5.76
## 63 23 m 7 30 16.66 19.83 6.79 4.72
## 64 24 m 7 30 17.42 18.44 6.86 4.55
## 65 25 m 7 30 15.80 21.36 7.89 4.45
## 66 26 m 7 30 14.60 18.81 6.10 3.72
## 67 27 f 7 30 15.62 19.22 7.90 4.82
## 68 28 f 7 30 17.82 18.59 6.78 4.33
## 69 29 f 7 30 19.22 21.98 8.82 5.61
## 70 30 f 7 30 15.55 19.15 7.56 4.16
## 71 31 f 7 30 19.03 21.61 7.61 4.63
## 72 32 m 7 30 17.42 20.25 7.79 4.00
## 73 33 m 7 30 17.01 20.22 8.33 4.12
## 74 34 m 7 30 18.78 20.09 7.11 4.38
## 75 35 f 7 30 20.96 20.51 7.27 5.82
## 76 36 f 7 30 18.90 19.70 7.80 4.87
## 77 37 7 30 17.33 20.79 7.49 4.19
## 78 38 m 7 30 20.44 22.07 7.21 4.12
## 79 39 f 7 30 19.78 18.90 9.86 4.84
## 81 1 9 15 17.48 21.60 6.84 4.11
## 82 2 m 9 15 29.88 22.92 8.46 5.15
## 83 3 f 9 15 27.50 22.62 7.96 4.90
## 84 4 m 9 15 21.63 23.31 8.15 4.31
## 85 5 f 9 15 35.06 25.57 8.38 5.20
## 86 6 m 9 15 24.57 22.90 8.34 4.66
## 87 7 m 9 15 36.20 23.52 8.49 4.99
## 88 8 9 15 22.65 19.77 7.82 5.43
## 89 9 m 9 15 31.22 21.43 8.30 4.23
## 90 10 f 9 15 34.84 22.64 9.11 4.25
## 91 11 f 9 15 29.30 22.99 8.05 4.09
## 92 12 m 9 15 24.49 21.40 7.21 4.72
## 93 13 f 9 15 25.63 22.13 8.45 4.71
## 94 14 f 9 15 25.36 23.44 8.28 4.88
## 95 15 m 9 15 19.76 20.69 9.10 4.99
## 96 16 f 9 15 38.91 23.77 9.16 4.87
## 97 17 f 9 15 28.12 22.39 7.29 4.71
## 98 18 m 9 15 20.53 19.80 6.04 3.95
## 99 19 f 9 15 30.00 25.40 7.69 4.19
## 100 20 m 9 15 26.54 20.41 8.99 4.36
## 101 21 m 9 30 31.89 22.27 7.81 3.78
## 102 22 f 9 30 38.62 25.12 8.86 5.08
## 103 23 m 9 30 35.36 29.99 8.04 4.81
## 104 24 m 9 30 26.88 23.02 7.96 4.88
## 105 25 m 9 30 23.00 21.82 7.83 5.01
## 106 26 m 9 30 22.80 21.13 7.94 4.29
## 107 27 f 9 30 23.96 22.35 8.13 4.15
## 108 28 f 9 30 29.65 22.96 8.64 4.92
## 109 29 f 9 30 25.71 24.41 8.74 4.25
## 110 30 f 9 30 21.80 21.23 8.04 4.71
## 111 31 f 9 30 29.67 23.64 7.74 4.78
## 112 32 m 9 30 27.06 24.15 7.75 4.70
## 113 33 m 9 30 29.08 20.45 7.97 4.46
## 114 34 m 9 30 28.00 21.85 8.16 4.37
## 115 35 f 9 30 30.00 23.16 8.92 5.17
## 116 36 f 9 30 25.40 21.74 7.64 5.13
## 117 37 9 30 23.54 22.22 7.64 4.58
## 118 38 m 9 30 30.86 24.72 8.33 5.25
## 119 39 f 9 30 31.08 22.74 6.68 5.51
## 121 1 11 15 18.58 20.02 7.97 4.43
## 122 2 m 11 15 42.83 24.15 8.23 4.38
## 123 3 f 11 15 35.46 22.87 9.77 5.38
## 124 4 m 11 15 29.60 23.30 7.90 4.92
## 125 5 f 11 15 51.10 27.93 9.48 6.42
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## 573 13 f 39 15 195.79 33.38 13.77 5.91
## 574 14 f 39 15 232.40 39.98 13.59 5.65
## 575 15 m 39 15 174.33 36.63 13.15 4.95
## 576 16 f 39 15 249.57 36.90 15.43 5.92
## 577 17 f 39 15 224.88 37.65 13.92 5.86
## 578 18 m 39 15 187.59 34.59 12.33 5.75
## 579 19 f 39 15 227.14 40.43 14.04 5.71
## 580 20 m 39 15 206.87 37.17 13.54 6.04
## 581 21 m 39 30 176.74 34.52 12.99 5.49
## 582 22 f 39 30 224.73 39.84 16.50 6.26
## 583 23 m 39 30 180.39 37.00 14.28 5.58
## 584 24 m 39 30 175.55 34.57 13.83 5.12
## 585 25 m 39 30 172.14 36.41 15.88 5.29
## 586 26 m 39 30 183.40 39.28 12.86 5.78
## 587 27 f 39 30 158.27 37.62 15.11 4.89
## 588 28 f 39 30 183.66 37.33 15.00 6.27
## 589 29 f 39 30 200.13 44.71 16.59 6.31
## 590 30 f 39 30 184.42 41.49 13.41 5.89
## 591 31 f 39 30 191.66 37.76 14.45 6.18
## 592 32 m 39 30 177.98 38.56 14.88 5.90
## 593 33 m 39 30 175.11 38.77 14.70 6.76
## 594 34 m 39 30 210.93 38.37 12.15 5.63
## 595 35 f 39 30 190.73 37.37 15.34 6.53
## 596 36 f 39 30 175.79 35.65 13.90 5.15
## 598 38 m 39 30 188.80 39.78 15.31 5.54
## 599 39 f 39 30 200.63 39.88 14.60 5.54
## 602 2 m 44 15 248.81 39.60 13.84 5.78
## 603 3 f 44 15 217.58 35.36 12.74 5.37
## 604 4 m 44 15 206.11 37.81 13.96 5.78
## 605 5 f 44 15 253.86 39.53 15.21 6.31
## 606 6 m 44 15 218.44 38.78 14.60 6.54
## 607 7 m 44 15 225.64 39.09 14.62 6.19
## 609 9 m 44 15 260.14 40.82 13.22 5.87
## 610 10 f 44 15 223.25 36.66 15.03 5.59
## 611 11 f 44 15 226.18 36.42 14.06 5.58
## 612 12 m 44 15 202.09 34.83 13.08 5.68
## 613 13 f 44 15 213.48 33.98 11.92 5.92
## 614 14 f 44 15 245.90 38.58 11.57 5.86
## 615 15 m 44 15 198.00 37.12 14.70 6.21
## 616 16 f 44 15 264.88 36.65 15.24 6.48
## 617 17 f 44 15 258.14 36.33 15.42 5.90
## 618 18 m 44 15 215.88 33.56 14.80 5.40
## 619 19 f 44 15 249.33 41.03 15.76 6.89
## 620 20 m 44 15 228.56 31.68 12.77 5.15
## 621 21 m 44 30 207.10 38.95 12.85 5.96
## 622 22 f 44 30 233.02 40.54 14.82 6.53
## 623 23 m 44 30 189.85 40.32 15.01 5.97
## 624 24 m 44 30 190.14 36.44 11.86 5.08
## 625 25 m 44 30 198.86 36.67 14.88 4.98
## 626 26 m 44 30 200.26 37.97 13.18 5.57
## 627 27 f 44 30 195.82 36.55 14.57 5.26
## 628 28 f 44 30 199.68 39.13 14.76 6.28
## 629 29 f 44 30 235.86 46.32 16.32 6.45
## 630 30 f 44 30 202.71 38.45 15.71 5.45
## 631 31 f 44 30 208.44 34.12 14.29 5.67
## 632 32 m 44 30 206.13 38.05 13.59 5.22
## 633 33 m 44 30 196.49 35.90 13.33 7.61
## 634 34 m 44 30 232.00 39.61 12.69 6.08
## 635 35 f 44 30 206.39 37.90 15.30 6.19
## 636 36 f 44 30 190.96 35.96 12.92 6.29
## 638 38 m 44 30 201.66 40.71 15.08 6.70
## 639 39 f 44 30 223.82 38.41 13.86 5.16
## 642 2 m 49 15 283.60 38.82 13.68 6.22
## 643 3 f 49 15 215.60 34.23 14.41 6.53
## 644 4 m 49 15 230.97 37.23 13.67 6.17
## 645 5 f 49 15 242.40 37.41 15.90 6.97
## 646 6 m 49 15 215.90 35.54 14.61 6.86
## 647 7 m 49 15 219.51 36.90 13.08 6.67
## 649 9 m 49 15 258.53 39.96 11.95 6.00
## 650 10 f 49 15 221.27 36.66 14.38 5.99
## 651 11 f 49 15 223.24 36.92 11.22 5.08
## 652 12 m 49 15 205.19 33.23 13.94 5.46
## 653 13 f 49 15 216.00 34.98 14.47 5.94
## 654 14 f 49 15 246.62 37.38 12.18 5.91
## 655 15 m 49 15 203.07 38.57 13.02 5.05
## 656 16 f 49 15 264.18 39.98 15.00 5.92
## 657 17 f 49 15 272.72 38.33 15.19 6.53
## 658 18 m 49 15 222.32 31.73 14.08 5.54
## 659 19 f 49 15 249.86 41.30 14.01 5.57
## 660 20 m 49 15 231.10 34.03 12.17 6.02
## 661 21 m 49 30 225.40 35.66 13.74 5.73
## 662 22 f 49 30 235.91 38.12 15.57 6.06
## 663 23 m 49 30 201.85 37.18 14.48 5.55
## 664 24 m 49 30 213.87 34.22 15.54 5.62
## 665 25 m 49 30 210.80 40.59 14.85 5.26
## 666 26 m 49 30 209.26 36.42 15.04 5.91
## 667 27 f 49 30 201.57 35.77 14.72 5.60
## 668 28 f 49 30 212.04 34.99 14.08 5.55
## 669 29 f 49 30 242.60 43.73 15.51 7.01
## 670 30 f 49 30 226.92 35.69 16.29 4.92
## 671 31 f 49 30 229.12 38.32 16.76 6.79
## 672 32 m 49 30 200.64 35.05 13.74 6.10
## 673 33 m 49 30 208.44 36.76 14.10 6.30
## 674 34 m 49 30 229.05 38.27 15.62 6.06
## 675 35 f 49 30 223.75 36.12 16.02 7.30
## 676 36 f 49 30 210.81 38.81 15.60 6.06
## 678 38 m 49 30 213.56 35.78 15.22 5.48
## 679 39 f 49 30 229.65 37.25 16.24 6.02
## 682 2 m 51 15 300.00 37.23 14.47 6.60
## 683 3 f 51 15 223.45 35.72 12.53 6.07
## 684 4 m 51 15 212.84 35.89 12.72 5.75
## 685 5 f 51 15 258.76 36.45 15.30 6.50
## 686 6 m 51 15 223.75 34.02 12.55 6.59
## 687 7 m 51 15 224.78 32.09 14.17 6.67
## 689 9 m 51 15 272.30 37.31 11.96 5.59
## 690 10 f 51 15 214.13 31.54 12.30 5.36
## 691 11 f 51 15 230.05 37.86 13.65 5.67
## 692 12 m 51 15 235.60 37.28 14.60 6.36
## 693 13 f 51 15 218.11 33.93 13.61 5.58
## 694 14 f 51 15 251.83 38.75 12.26 6.60
## 695 15 m 51 15 212.82 33.02 13.73 5.55
## 696 16 f 51 15 270.04 37.80 15.49 6.17
## 697 17 f 51 15 280.75 40.06 14.16 6.03
## 698 18 m 51 15 231.80 34.70 11.44 5.95
## 699 19 f 51 15 264.00 38.49 15.16 6.75
## 700 20 m 51 15 238.32 36.80 13.36 5.84
## 701 21 m 51 30 224.06 34.54 14.31 6.18
## 702 22 f 51 30 243.85 37.81 14.41 6.44
## 703 23 m 51 30 208.60 37.04 12.91 6.10
## 704 24 m 51 30 205.55 37.07 12.92 6.36
## 705 25 m 51 30 216.43 37.80 15.00 5.86
## 706 26 m 51 30 210.10 36.49 13.60 5.66
## 707 27 f 51 30 205.86 39.15 15.85 5.96
## 708 28 f 51 30 214.85 36.58 13.39 6.66
## 709 29 f 51 30 258.06 43.08 16.42 7.40
## 710 30 f 51 30 218.36 36.13 15.41 7.58
## 711 31 f 51 30 222.30 34.16 15.56 6.60
## 712 32 m 51 30 212.17 36.04 14.05 5.83
## 713 33 m 51 30 215.82 37.71 15.00 5.76
## 714 34 m 51 30 243.19 36.79 16.68 5.46
## 715 35 f 51 30 230.75 39.80 14.02 7.35
## 716 36 f 51 30 202.89 37.73 14.86 5.76
## 718 38 m 51 30 219.18 37.17 13.73 5.92
## 719 39 f 51 30 240.80 39.33 13.94 5.88
## 722 2 m 66 15 313.35 39.45 13.84 7.22
## 723 3 f 66 15 278.90 35.58 14.32 6.24
## 724 4 m 66 15 236.60 38.70 13.06 5.60
## 725 5 f 66 15 312.77 37.35 15.39 6.66
## 726 6 m 66 15 238.78 32.17 12.70 8.02
## 727 7 m 66 15 238.52 36.23 15.13 7.24
## 729 9 m 66 15 202.34 39.10 15.18 6.16
## 730 10 f 66 15 265.84 38.06 14.90 5.84
## 731 11 f 66 15 245.58 38.60 12.64 6.71
## 732 12 m 66 15 243.32 32.58 12.83 6.28
## 733 13 f 66 15 282.37 32.70 14.93 5.84
## 734 14 f 66 15 269.85 40.75 14.08 5.52
## 735 15 m 66 15 230.36 35.33 13.14 6.06
## 736 16 f 66 15 289.70 35.48 14.87 6.78
## 737 17 f 66 15 370.68 38.05 16.16 6.65
## 738 18 m 66 15 245.09 34.90 13.08 5.36
## 739 19 f 66 15 311.78 40.98 14.49 5.79
## 740 20 m 66 15 254.78 47.52 15.45 6.81
## 741 21 m 66 30 256.27 36.62 13.60 6.34
## 742 22 f 66 30 294.21 38.83 16.27 6.48
## 743 23 m 66 30 232.59 39.16 14.12 6.44
## 744 24 m 66 30 200.65 33.68 15.03 6.47
## 745 25 m 66 30 217.38 38.00 16.20 5.31
## 746 26 m 66 30 226.22 39.45 12.51 4.99
## 747 27 f 66 30 248.14 36.56 14.75 6.19
## 748 28 f 66 30 254.29 32.58 13.66 5.30
## 749 29 f 66 30 311.70 43.36 15.70 6.60
## 750 30 f 66 30 281.47 42.04 16.83 6.26
## 751 31 f 66 30 275.33 37.35 14.45 5.90
## 752 32 m 66 30 210.13 36.95 14.28 5.58
## 753 33 m 66 30 252.11 39.15 12.45 6.83
## 754 34 m 66 30 254.25 36.86 16.07 5.64
## 755 35 f 66 30 258.18 39.23 17.67 7.93
## 756 36 f 66 30 253.89 37.15 14.55 4.83
## 758 38 m 66 30 237.70 41.04 14.16 7.04
## 759 39 f 66 30 288.04 37.56 15.88 5.79
## 762 2 m 80 15 300.00 40.06 14.30 6.54
## 764 4 m 80 15 254.35 38.35 14.81 8.41
## 765 5 f 80 15 314.00 34.45 15.72 7.28
## 766 6 m 80 15 240.77 36.71 16.02 5.78
## 767 7 m 80 15 253.45 34.86 14.53 7.65
## 769 9 m 80 15 318.00 38.60 16.26 9.52
## 770 10 f 80 15 270.05 37.70 15.00 5.95
## 771 11 f 80 15 259.48 35.24 13.99 6.97
## 772 12 m 80 15 250.00 31.28 13.26 5.74
## 773 13 f 80 15 277.36 35.69 14.89 6.52
## 774 14 f 80 15 312.65 38.99 13.97 6.16
## 775 15 m 80 15 242.29 34.39 14.76 7.36
## 777 17 f 80 15 334.68 38.55 16.82 6.54
## 778 18 m 80 15 246.26 33.78 12.67 5.85
## 779 19 f 80 15 294.60 38.81 15.29 7.62
## 780 20 m 80 15 266.39 36.34 15.65 6.08
## 781 21 m 80 30 245.18 39.50 13.95 6.02
## 782 22 f 80 30 297.74 38.29 15.96 6.59
## 783 23 m 80 30 243.70 38.29 16.41 6.31
## 784 24 m 80 30 210.40 37.14 15.84 5.46
## 785 25 m 80 30 215.14 37.63 17.30 5.28
## 786 26 m 80 30 228.50 40.10 14.22 5.77
## 787 27 f 80 30 244.05 41.64 13.22 6.70
## 788 28 f 80 30 228.80 36.58 15.42 5.66
## 789 29 f 80 30 327.46 49.42 15.15 6.99
## 790 30 f 80 30 274.58 38.52 16.50 6.64
## 791 31 f 80 30 261.37 39.52 15.79 6.02
## 792 32 m 80 30 219.82 36.55 13.12 5.89
## 793 33 m 80 30 262.89 38.41 14.74 7.05
## 794 34 m 80 30 254.42 41.48 14.90 6.04
## 795 35 f 80 30 259.30 41.36 16.15 7.30
## 796 36 f 80 30 246.17 36.26 14.22 5.12
## 798 38 m 80 30 246.96 38.89 15.87 6.16
## 799 39 f 80 30 269.89 40.32 14.99 5.34
## 842 2 m 123 15 314.00 39.90 16.17 5.48
## 843 3 f 123 15 306.00 36.71 15.20 6.40
## 844 4 m 123 15 252.50 37.97 13.32 4.71
## 845 5 f 123 15 321.50 43.52 16.65 6.76
## 846 6 m 123 15 241.00 36.35 16.30 5.72
## 847 7 m 123 15 257.00 34.92 15.23 6.22
## 849 9 m 123 15 318.00 40.49 16.62 6.54
## 850 10 f 123 15 298.00 37.88 15.66 6.36
## 851 11 f 123 15 323.50 37.81 13.45 6.75
## 852 12 m 123 15 250.00 37.24 14.49 5.13
## 853 13 f 123 15 288.00 35.16 16.39 5.38
## 854 14 f 123 15 303.00 39.42 14.33 6.86
## 855 15 m 123 15 246.50 38.03 16.69 5.53
## 857 17 f 123 15 361.00 40.15 15.22 7.80
## 859 19 f 123 15 297.00 42.75 16.07 6.41
## 860 20 m 123 15 255.00 35.86 15.37 6.62
## 861 21 m 123 30 264.00 36.03 15.76 5.64
## 862 22 f 123 30 321.00 40.14 16.30 6.80
## 863 23 m 123 30 254.00 39.23 15.10 6.02
## 864 24 m 123 30 224.00 38.07 15.83 5.78
## 865 25 m 123 30 223.50 36.99 16.72 6.05
## 866 26 m 123 30 235.00 38.71 15.41 5.72
## 867 27 f 123 30 278.50 39.03 16.22 6.22
## 868 28 f 123 30 251.50 39.07 14.71 7.03
## 869 29 f 123 30 375.00 45.32 18.14 6.44
## 870 30 f 123 30 304.50 39.22 15.59 5.53
## 871 31 f 123 30 290.00 37.93 16.04 6.34
## 872 32 m 123 30 228.50 37.28 15.76 5.91
## 873 33 m 123 30 261.50 39.30 13.78 5.56
## 874 34 m 123 30 273.50 37.17 17.36 5.71
## 875 35 f 123 30 279.50 39.61 15.15 7.51
## 876 36 f 123 30 291.00 38.78 16.98 6.49
## 878 38 m 123 30 256.00 38.98 16.44 6.26
## 879 39 f 123 30 286.50 39.32 14.73 5.93
## width_mm NOTES
## 1 4.49
## 2 4.44
## 3 4.01
## 4 4.22
## 5 4.56
## 6 3.73
## 7 4.60
## 8 4.66
## 9 3.83
## 10 3.89
## 11 4.53
## 12 3.89
## 13 3.91
## 14 4.12
## 15 3.70
## 16 4.25
## 17 4.28
## 18 3.92
## 19 4.44
## 20 4.39
## 21 3.81
## 22 4.16
## 23 4.34
## 24 4.29
## 25 4.04
## 26 4.09
## 27 3.96
## 28 4.07
## 29 4.06
## 30 3.97
## 31 4.00
## 32 4.22
## 33 4.27
## 34 4.15
## 35 4.36
## 36 4.57
## 37 4.03
## 38 4.44
## 39 3.29
## 40 3.97
## 41 4.05
## 42 4.41
## 43 3.71
## 44 4.21
## 45 3.52
## 46 4.44
## 47 4.53
## 48 3.86
## 49 4.25
## 50 3.99
## 51 4.83
## 52 4.10
## 53 4.50
## 54 4.25
## 55 3.98
## 56 4.45
## 57 4.60
## 58 3.84
## 59 4.00
## 60 4.31
## 61 4.14
## 62 4.86
## 63 4.75
## 64 3.64
## 65 4.22
## 66 4.06
## 67 4.28
## 68 3.76
## 69 4.14
## 70 4.41
## 71 3.72
## 72 4.06
## 73 4.91
## 74 3.92
## 75 4.55
## 76 4.21
## 77 4.27
## 78 4.01
## 79 3.67
## 81 4.54
## 82 4.29
## 83 4.20
## 84 4.18
## 85 4.51
## 86 4.25
## 87 4.35
## 88 4.21
## 89 3.88
## 90 4.11
## 91 4.42
## 92 4.03
## 93 4.64
## 94 4.30
## 95 3.89
## 96 4.88
## 97 4.46
## 98 3.88
## 99 4.44
## 100 3.65
## 101 4.37
## 102 4.45
## 103 4.68
## 104 4.10
## 105 3.83
## 106 4.14
## 107 4.26
## 108 4.20
## 109 4.76
## 110 4.32
## 111 3.80
## 112 4.49
## 113 4.70
## 114 4.59
## 115 4.82
## 116 4.27
## 117 4.41
## 118 4.14
## 119 4.27
## 121 4.77
## 122 4.48
## 123 4.29
## 124 4.56
## 125 4.96
## 126 4.53
## 127 5.85
## 128 4.68
## 129 5.13
## 130 4.66
## 131 4.59
## 132 4.60
## 133 4.35
## 134 4.77
## 135 5.07
## 136 5.01
## 137 4.46
## 138 4.44
## 139 4.60
## 140 4.59
## 141 4.31
## 142 4.29
## 143 4.07
## 144 3.94
## 145 4.74
## 146 4.09
## 147 4.22
## 148 4.49
## 149 4.54
## 150 4.36
## 151 4.45
## 152 4.75
## 153 4.50
## 154 4.38
## 155 5.10
## 156 4.86
## 157 4.99
## 158 4.32
## 159 4.22
## 162 4.53
## 163 5.21
## 164 4.35
## 165 4.57
## 166 4.89
## 167 4.93
## 169 4.72
## 170 3.88
## 171 4.53
## 172 4.00
## 173 4.24
## 174 4.99
## 175 4.12
## 176 4.18
## 177 5.04
## 178 4.64
## 179 4.30
## 180 5.34
## 181 4.56
## 182 5.18
## 183 4.32
## 184 4.92
## 185 4.90
## 186 4.10
## 187 4.88
## 188 5.00
## 189 5.15
## 190 4.98
## 191 5.20
## 192 4.23
## 193 4.76
## 194 5.01
## 195 5.70
## 196 4.66
## 197 4.98
## 198 4.34
## 199 4.30
## 202 5.61
## 203 4.05
## 204 5.07
## 205 4.25
## 206 5.72
## 207 5.10
## 209 5.07
## 210 4.93
## 211 4.18
## 212 4.68
## 213 4.24
## 214 4.71
## 215 4.67
## 216 5.15
## 217 5.39
## 218 4.38
## 219 4.11
## 220 4.54
## 221 4.14
## 222 4.92
## 223 5.22
## 224 4.25
## 225 4.05
## 226 4.64
## 227 4.64
## 228 4.89
## 229 4.98
## 230 4.77
## 231 5.02
## 232 4.23
## 233 5.01
## 234 4.71
## 235 3.70
## 236 4.65
## 238 4.55
## 239 5.37
## 242 5.33
## 243 4.26
## 244 5.25
## 245 4.97
## 246 4.02
## 247 5.34
## 249 4.78
## 250 4.63
## 251 5.40
## 252 4.08
## 253 3.74
## 254 4.24
## 255 4.02
## 256 4.44
## 257 5.42
## 258 4.75
## 259 4.65
## 260 5.38
## 261 4.46
## 262 5.06
## 263 4.63
## 264 5.10
## 265 5.06
## 266 5.64
## 267 4.80
## 268 5.10
## 269 5.64
## 270 4.82
## 271 4.56
## 272 4.28
## 273 4.74
## 274 4.50
## 275 5.66
## 276 5.40
## 278 5.33
## 279 5.30
## 282 5.46
## 283 4.19
## 284 4.37
## 285 5.51
## 286 4.63
## 287 5.22
## 289 4.34
## 290 4.32
## 291 5.10
## 292 4.61
## 293 4.55
## 294 4.63
## 295 5.05
## 296 5.68
## 297 4.94
## 298 4.96
## 299 4.93
## 300 4.80
## 301 5.54
## 302 4.59
## 303 5.23
## 304 4.05
## 305 4.52
## 306 4.93
## 307 5.31
## 308 4.80
## 309 4.57
## 310 4.57
## 311 4.32
## 312 4.76
## 313 5.34
## 314 4.92
## 315 5.03
## 316 4.65
## 318 4.81
## 319 5.00
## 322 5.02
## 323 5.20
## 324 5.18
## 325 5.40
## 326 5.58
## 327 5.31
## 329 5.76
## 330 5.36
## 331 4.78
## 332 4.69
## 333 5.00
## 334 5.04
## 335 5.97
## 336 5.57
## 337 5.48
## 338 5.15
## 339 5.12
## 340 4.87
## 341 4.37
## 342 5.39
## 343 4.68
## 344 4.50
## 345 5.07
## 346 4.32
## 347 4.46
## 348 4.96
## 349 5.55
## 350 5.20
## 351 4.86
## 352 5.06
## 353 4.58
## 354 6.25
## 355 5.40
## 356 4.88
## 358 4.13
## 359 5.09
## 362 4.17
## 363 4.97
## 364 4.91
## 365 5.06
## 366 5.49
## 367 5.08
## 369 5.38
## 370 5.70
## 371 5.64
## 372 4.77
## 373 4.83
## 374 5.14
## 375 4.76
## 376 5.15
## 377 5.49
## 378 5.06
## 379 4.80
## 380 5.03
## 381 5.40
## 382 4.82
## 383 4.74
## 384 4.69
## 385 4.60
## 386 4.52
## 387 4.82
## 388 4.55
## 389 5.30
## 390 4.47
## 391 4.89
## 392 5.09
## 393 5.03
## 394 5.21
## 395 4.70
## 396 4.51
## 398 5.05
## 399 4.84
## 402 4.78
## 403 4.46
## 404 4.31
## 405 5.11
## 406 4.41
## 407 5.64
## 409 5.03
## 410 3.99
## 411 4.70
## 412 4.43
## 413 4.75
## 414 4.71
## 415 5.43
## 416 5.38
## 417 3.90
## 418 3.72
## 419 4.86
## 420 4.74
## 421 4.98
## 422 4.13
## 423 5.47
## 424 5.11
## 425 4.71
## 426 4.96
## 427 4.95
## 428 5.28
## 429 5.19
## 430 4.61
## 431 4.93
## 432 5.39
## 433 5.12
## 434 5.17
## 435 5.64
## 436 5.54
## 438 4.10
## 439 4.95
## 442 5.35
## 443 4.91
## 444 4.85
## 445 4.50
## 446 4.47
## 447 4.43
## 449 5.01
## 450 4.87
## 451 4.90
## 452 4.60
## 453 4.97
## 454 5.26
## 455 4.57
## 456 5.41
## 457 4.40
## 458 4.87
## 459 4.57
## 460 4.54
## 461 3.92
## 462 5.28
## 463 5.30
## 464 5.03
## 465 5.15
## 466 5.00
## 467 5.78
## 468 5.74
## 469 6.12
## 470 4.89
## 471 5.05
## 472 4.90
## 473 5.04
## 474 4.56
## 475 5.00
## 476 5.64
## 478 4.54
## 479 4.77
## 482 5.70
## 483 5.02
## 484 4.93
## 485 4.73
## 486 5.08
## 487 4.89
## 489 5.18
## 490 4.85
## 491 5.12
## 492 4.55
## 493 4.96
## 494 4.74
## 495 4.36
## 496 4.79
## 497 5.23
## 498 5.41
## 499 5.21
## 500 4.87
## 501 4.96
## 502 4.57
## 503 5.57
## 504 5.31
## 505 5.23
## 506 5.64
## 507 5.50
## 508 4.90
## 509 5.91
## 510 5.46
## 511 5.31
## 512 6.25
## 513 5.41
## 514 6.07
## 515 5.55
## 516 5.81
## 518 5.10
## 519 5.02
## 522 5.56
## 523 4.79
## 524 6.29
## 525 4.99
## 526 5.45
## 527 5.78
## 529 5.73
## 530 4.92
## 531 4.69
## 532 4.75
## 533 4.96
## 534 4.59
## 535 5.00
## 536 4.89
## 537 4.39
## 538 4.61
## 539 4.33
## 540 4.67
## 541 4.98
## 542 4.47
## 543 5.23
## 544 5.07
## 545 5.56
## 546 4.87
## 547 5.44
## 548 5.58
## 549 6.03
## 550 4.89
## 551 4.99
## 552 4.99
## 553 5.25
## 554 5.29
## 555 4.90
## 556 5.15
## 558 4.65
## 559 4.95
## 562 5.03
## 563 4.44
## 564 4.33
## 565 5.70
## 566 5.18
## 567 5.43
## 569 4.58
## 570 4.74
## 571 5.18
## 572 5.05
## 573 4.57
## 574 5.50
## 575 5.23
## 576 5.80
## 577 4.55
## 578 4.38
## 579 6.12
## 580 4.80
## 581 5.02
## 582 5.06
## 583 5.43
## 584 4.48
## 585 4.72
## 586 5.47
## 587 5.44
## 588 4.83
## 589 4.75
## 590 4.45
## 591 5.02
## 592 5.06
## 593 4.31
## 594 4.39
## 595 4.61
## 596 5.00
## 598 5.15
## 599 5.05
## 602 4.73
## 603 4.39
## 604 4.75
## 605 4.74
## 606 4.35
## 607 4.33
## 609 5.03
## 610 4.26
## 611 5.80
## 612 5.48
## 613 5.30
## 614 5.19
## 615 5.00
## 616 5.06
## 617 5.74
## 618 4.40
## 619 5.29
## 620 4.49
## 621 4.99
## 622 5.28
## 623 4.52
## 624 4.18
## 625 4.46
## 626 4.24
## 627 5.72
## 628 4.82
## 629 4.78
## 630 4.09
## 631 4.43
## 632 5.02
## 633 5.31
## 634 5.19
## 635 5.36
## 636 4.37
## 638 5.14
## 639 5.10
## 642 5.65
## 643 4.91
## 644 4.34
## 645 5.14
## 646 5.89
## 647 5.07
## 649 4.93
## 650 4.50
## 651 5.01
## 652 5.14
## 653 4.58
## 654 4.53
## 655 5.30
## 656 4.87
## 657 6.67
## 658 4.43
## 659 5.17
## 660 5.33
## 661 4.67
## 662 4.93
## 663 4.92
## 664 3.63
## 665 4.47
## 666 4.89
## 667 4.20
## 668 5.05
## 669 5.50
## 670 4.77
## 671 4.83
## 672 4.66
## 673 4.65
## 674 5.35
## 675 4.76
## 676 4.70
## 678 4.45
## 679 5.04
## 682 5.43
## 683 4.95
## 684 3.78
## 685 5.45
## 686 4.86
## 687 5.27
## 689 5.61
## 690 5.45
## 691 5.53
## 692 5.56
## 693 4.66
## 694 5.30
## 695 4.57
## 696 4.99
## 697 5.71
## 698 5.67
## 699 4.24
## 700 3.70
## 701 5.33
## 702 5.04
## 703 5.56
## 704 4.40
## 705 4.92
## 706 4.50
## 707 5.02
## 708 5.13
## 709 5.66
## 710 5.41
## 711 5.52
## 712 5.43
## 713 5.30
## 714 4.82
## 715 5.10
## 716 5.23
## 718 5.34
## 719 5.11
## 722 5.34
## 723 4.93
## 724 4.88
## 725 5.68
## 726 5.02
## 727 5.03
## 729 4.84
## 730 4.98
## 731 5.65
## 732 5.41
## 733 5.03
## 734 4.57
## 735 5.36
## 736 5.09
## 737 5.23
## 738 4.87
## 739 5.43
## 740 5.06
## 741 4.59
## 742 5.45
## 743 4.81
## 744 4.92
## 745 4.85
## 746 4.98
## 747 4.72
## 748 4.12
## 749 5.60
## 750 5.27
## 751 5.77
## 752 5.46
## 753 4.86
## 754 4.67
## 755 5.15
## 756 4.93
## 758 5.44
## 759 4.36
## 762 4.78
## 764 4.81
## 765 5.23
## 766 4.72
## 767 6.07
## 769 4.55
## 770 5.46
## 771 4.46
## 772 5.32
## 773 5.52
## 774 4.89
## 775 6.14
## 777 4.26
## 778 4.47
## 779 5.95
## 780 5.83
## 781 4.03
## 782 4.50
## 783 4.93
## 784 5.45
## 785 4.25
## 786 5.65
## 787 5.37
## 788 5.43
## 789 6.92
## 790 5.14
## 791 5.34
## 792 5.27
## 793 5.50
## 794 5.50
## 795 5.50
## 796 5.61
## 798 5.27
## 799 5.03
## 842 4.64
## 843 5.76
## 844 4.14
## 845 4.80
## 846 5.80
## 847 4.90
## 849 4.78
## 850 5.12
## 851 4.94
## 852 4.83
## 853 5.01
## 854 5.00
## 855 4.55
## 857 4.99
## 859 4.56
## 860 4.61
## 861 4.18
## 862 4.83
## 863 5.16
## 864 4.16
## 865 5.44
## 866 4.84
## 867 4.38
## 868 5.48
## 869 5.22
## 870 5.10
## 871 4.95
## 872 4.75
## 873 4.90
## 874 4.96
## 875 5.34
## 876 5.06
## 878 5.69
## 879 4.195a) Three fits (10 points) To begin with, I’d like you to fit the relationship that describes how Tarsus (leg) length predicts upper beak (Culmen) length. Fit this relationship using least squares, likelihood, and Bayesian techniques. For each fit, demonstrate that the necessary assumptions have been met. Note, functions used to fit with likelihood and Bayes may or may not behave well when fed NAs. So look out for those errors.
#LEAST SQUARES####
ggplot(data= morphology, mapping=aes(x=tarsus_mm,
y=culmen_mm)) +
geom_point() #first graph the relationship of tarsus on culmen
lm_morph <- lm(data=morphology, culmen_mm~tarsus_mm) #fit a lm to find slope/ y-int
lm_morph #y-int = -0.09871 slope= 0.37293 ##
## Call:
## lm(formula = culmen_mm ~ tarsus_mm, data = morphology)
##
## Coefficients:
## (Intercept) tarsus_mm
## -0.09871 0.37293summary(lm_morph)##
## Call:
## lm(formula = culmen_mm ~ tarsus_mm, data = morphology)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4081 -0.7029 -0.0328 0.7263 3.5970
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.098707 0.215450 -0.458 0.647
## tarsus_mm 0.372927 0.006646 56.116 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.238 on 764 degrees of freedom
## Multiple R-squared: 0.8048, Adjusted R-squared: 0.8045
## F-statistic: 3149 on 1 and 764 DF, p-value: < 2.2e-16#plot the data from above but add in line with the slope found from our linear model found above
plot(data = morphology, culmen_mm~tarsus_mm) +
abline(lm_morph)
## integer(0)#run cor test to see if tarsus does influence culmen length
cor.test(morphology$culmen_mm, morphology$tarsus_mm) ##
## Pearson's product-moment correlation
##
## data: morphology$culmen_mm and morphology$tarsus_mm
## t = 56.116, df = 764, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.8823111 0.9100845
## sample estimates:
## cor
## 0.8970803#get 0.8970803 so there seems to be a strong corr. Reject null that says no correlation
plot(lm_morph, which=2) #look at qq plot. See there is some dev from line at both ends
plot(lm_morph, which=5) #cooks distance makes me think we get some var as we move out due to having fewer birds with large tarsus lengths
#LIKELIHOOD####
#initial visualization to determine if lm is appropriate
ggplot(data= morphology, mapping=aes(x=tarsus_mm,
y=culmen_mm)) +
geom_point() #is there relation between x and y var... seems like it! so we'll fit that model
morph_mod <- glm(culmen_mm ~ tarsus_mm, #create a glm with (y~x)
family = gaussian(link = "identity"), #identity b/c not transforming our data
data=morphology)
morph_mod##
## Call: glm(formula = culmen_mm ~ tarsus_mm, family = gaussian(link = "identity"),
## data = morphology)
##
## Coefficients:
## (Intercept) tarsus_mm
## -0.09871 0.37293
##
## Degrees of Freedom: 765 Total (i.e. Null); 764 Residual
## Null Deviance: 6001
## Residual Deviance: 1172 AIC: 2505#assumptions
morph_fit <- predict(morph_mod) #predictions from the model create above
morph_fit## 1 2 3 4 5 6 7 8
## 7.128614 7.501540 7.001819 7.400850 8.038555 7.296431 7.975157 6.684831
## 9 10 11 12 13 14 15 16
## 7.136072 7.699192 7.348640 6.834002 6.863836 7.598501 6.699748 7.952782
## 17 18 19 20 21 22 23 24
## 7.449331 6.487180 7.494082 6.613975 7.203199 8.232477 6.807897 7.068945
## 25 26 27 28 29 30 31 32
## 7.445601 7.054028 6.587870 7.635794 8.098223 6.871294 7.535104 7.371016
## 33 34 35 36 37 38 39 40
## 7.247950 7.206928 7.229304 7.292701 7.702921 7.087592 7.132343 6.994360
## 41 42 43 44 45 46 47 48
## 6.807897 7.318806 7.594772 7.329994 7.068945 7.143531 8.568111 6.897399
## 49 50 51 52 53 54 55 56
## 7.825987 7.441872 7.009277 8.325709 7.523916 5.938977 6.904858 8.624050
## 57 58 59 60 61 62 63 64
## 8.221289 6.696019 8.008721 7.326265 7.244221 8.325709 7.296431 6.778063
## 65 66 67 68 69 70 71 72
## 7.867009 6.916045 7.068945 6.834002 8.098223 7.042841 7.960240 7.453060
## 73 74 75 76 77 78 79 81
## 7.441872 7.393392 7.550021 7.247950 7.654440 8.131787 6.949609 7.956511
## 82 83 84 85 86 87 88 89
## 8.448774 8.336896 8.594216 9.437030 8.441316 8.672531 7.274055 7.893114
## 90 91 92 93 94 95 96 97
## 8.344355 8.474879 7.881926 8.154162 8.642696 7.617148 8.765762 8.251123
## 98 99 100 101 102 103 104 105
## 7.285243 9.373633 7.512728 8.206372 9.269213 11.085367 8.486067 8.038555
## 106 107 108 109 110 111 112 113
## 7.781236 8.236206 8.463692 9.004435 7.818528 8.717282 8.907474 7.527645
## 114 115 116 117 118 119 121 122
## 8.049743 8.538277 8.008721 8.187726 9.120043 8.381648 7.367287 8.907474
## 123 124 125 126 127 128 129 130
## 8.430128 8.590487 10.317138 8.706094 9.630952 7.591043 9.272943 9.291589
## 131 132 133 134 135 136 137 138
## 9.157335 8.422670 8.437587 8.929850 8.113140 9.724184 9.011894 8.258582
## 139 140 141 142 143 144 145 146
## 8.892557 12.629284 10.007608 9.616035 8.624050 9.347528 8.735928 8.247394
## 147 148 149 150 151 152 153 154
## 8.918662 9.377362 9.862167 8.512172 9.299047 8.534548 9.108855 9.030540
## 155 156 157 158 159 162 163 164
## 9.194628 8.877640 8.381648 9.321423 7.889384 10.018796 9.041728 8.247394
## 165 166 167 169 170 171 172 173
## 10.842964 8.844077 10.279845 10.044901 9.809957 9.261755 8.967143 8.996977
## 174 175 176 177 178 179 180 181
## 9.112584 8.788138 10.630396 9.489240 7.844633 9.988962 8.273499 9.947940
## 182 183 184 185 186 187 188 189
## 11.312852 10.022525 9.828604 9.746560 9.537721 8.366731 10.250011 10.320867
## 190 191 192 193 194 195 196 197
## 9.202087 9.377362 10.320867 10.097111 9.727913 9.123772 9.604847 9.750289
## 198 199 202 203 204 205 206 207
## 9.604847 10.242552 10.242552 9.690621 9.660786 10.992135 9.205816 10.898903
## 209 210 211 212 213 214 215 216
## 10.410369 10.126945 9.716725 9.000706 9.336340 10.059818 7.632065 11.633569
## 217 218 219 220 221 222 223 224
## 9.754018 8.482338 10.235094 9.302777 10.231364 11.223350 9.649599 9.992691
## 225 226 227 228 229 230 231 232
## 10.033713 9.079021 10.414099 9.899460 10.719898 9.798769 9.224462 10.302221
## 233 234 235 236 238 239 242 243
## 9.996421 10.432745 10.566999 9.321423 9.668245 10.675147 10.958572 10.257469
## 244 245 246 247 249 250 251 252
## 11.245725 11.816303 9.843521 11.596276 11.100284 11.689508 10.932467 9.310235
## 253 254 255 256 257 258 259 260
## 9.451947 10.481225 8.970872 10.235094 10.074735 9.537721 10.716169 10.272386
## 261 262 263 264 265 266 267 268
## 9.992691 12.595720 9.988962 10.492413 10.772108 10.238823 9.433301 10.268657
## 269 270 271 272 273 274 275 276
## 10.995864 10.231364 9.668245 10.645313 10.059818 10.525977 10.742274 9.996421
## 278 279 282 283 284 285 286 287
## 11.573901 11.786469 11.458294 10.395452 10.343242 12.580803 14.609525 10.298491
## 289 290 291 292 293 294 295 296
## 11.036886 12.043789 11.581359 9.627223 9.492969 10.123216 9.082750 12.677764
## 297 298 299 300 301 302 303 304
## 10.790755 10.108299 10.563269 10.011338 10.634125 12.200418 11.976662 10.343242
## 305 306 307 308 309 310 311 312
## 10.939925 10.921279 10.529706 9.869625 11.764093 10.466308 10.876528 10.402911
## 313 314 315 316 318 319 322 323
## 11.085367 10.682606 11.350145 10.708711 12.058706 12.618096 11.737989 11.014511
## 324 325 326 327 329 330 331 332
## 11.622381 13.349032 11.428459 12.778454 11.156223 12.375693 11.823762 10.406640
## 333 334 335 336 337 338 339 340
## 10.350701 11.678320 9.597389 12.442820 11.723072 10.059818 11.488128 11.816303
## 341 342 343 344 345 346 347 348
## 11.450835 12.722515 11.260642 11.696967 13.099171 11.171140 11.182328 11.100284
## 349 350 351 352 353 354 355 356
## 12.946271 11.655945 10.936196 10.783296 11.939369 12.979835 10.708711 10.816859
## 358 359 362 363 364 365 366 367
## 12.573345 12.625554 12.797101 8.672531 11.379979 13.460910 12.088540 13.024586
## 369 370 371 372 373 374 375 376
## 12.207876 13.024586 14.322371 10.947384 10.787025 11.670862 9.112584 13.121547
## 377 378 379 380 381 382 383 384
## 10.455120 11.126389 12.897791 11.946828 12.137020 13.058149 11.946828 12.506218
## 385 386 387 388 389 390 391 392
## 13.244613 12.353318 11.663403 12.908979 13.591435 11.678320 12.647930 12.338401
## 393 394 395 396 398 399 402 403
## 11.730530 12.715057 12.200418 12.718786 12.808288 13.184944 13.326657 12.084810
## 404 405 406 407 409 410 411 412
## 12.327213 14.150825 12.118374 13.509391 13.177486 12.640471 12.737432 11.443376
## 413 414 415 416 417 418 419 420
## 11.432189 11.909535 11.107742 13.114088 11.805115 11.130118 13.826378 12.084810
## 421 422 423 424 425 426 427 428
## 12.983564 13.326657 13.147652 12.968647 13.117818 12.785913 11.976662 12.894062
## 429 430 431 432 433 434 435 436
## 15.109247 13.211049 12.752349 13.598893 12.953730 13.852483 13.804003 13.065608
## 438 439 442 443 444 445 446 447
## 13.438535 13.367679 13.736876 12.841852 12.334671 14.777342 13.718230 14.389498
## 449 450 451 452 453 454 455 456
## 13.218508 12.666576 13.554142 12.002767 11.875971 13.102901 11.816303 13.930798
## 457 458 459 460 461 462 463 464
## 12.349588 11.883430 13.554142 11.059262 12.961188 14.292537 12.588262 13.345303
## 465 466 467 468 469 470 471 472
## 13.628727 13.487015 12.054976 12.785913 15.567947 13.494474 13.662291 12.744891
## 473 474 475 476 478 479 482 483
## 12.912708 13.211049 12.424174 12.845581 13.449722 13.796544 13.099171 11.387437
## 484 485 486 487 489 490 491 492
## 13.401242 13.826378 13.017127 13.960632 14.299995 13.173757 13.956903 11.644757
## 493 494 495 496 497 498 499 500
## 12.517406 13.624998 12.095998 14.408144 12.841852 11.894618 14.732591 12.081081
## 501 502 503 504 505 506 507 508
## 12.946271 14.553586 13.602622 13.248342 13.748064 13.244613 12.845581 13.386325
## 509 510 511 512 513 514 515 516
## 15.530654 13.445993 12.819476 13.557871 12.901520 13.900964 14.244056 13.147652
## 518 519 522 523 524 525 526 527
## 14.400686 13.729418 14.855656 12.614366 13.479557 14.766154 13.833837 13.725688
## 529 530 531 532 533 534 535 536
## 14.467813 14.482730 13.774169 12.882874 12.834393 14.396956 12.614366 14.221681
## 537 538 539 540 541 542 543 544
## 14.534939 12.591991 15.314356 13.378866 13.449722 14.672922 14.684110 14.486459
## 545 546 547 548 549 550 551 552
## 13.132735 14.579691 13.822649 13.375137 16.548744 14.415603 14.050135 14.437978
## 553 554 555 556 558 559 562 563
## 13.807732 14.262703 15.112976 14.885491 14.061322 14.035217 14.531210 13.203591
## 564 565 566 567 569 570 571 572
## 14.143366 13.628727 13.975549 14.139637 14.721403 13.214779 13.266988 12.856769
## 573 574 575 576 577 578 579 580
## 12.349588 14.810905 13.561600 13.662291 13.941986 12.800830 14.978722 13.762981
## 581 582 583 584 585 586 587 588
## 12.774725 14.758695 13.699583 12.793371 13.479557 14.549856 13.930798 13.822649
## 589 590 591 592 593 594 595 596
## 16.574849 15.374025 13.983008 14.281349 14.359664 14.210493 13.837566 13.196132
## 598 599 602 603 604 605 606 607
## 14.736320 14.773612 14.669193 13.087983 14.001654 14.643088 14.363393 14.479000
## 609 610 611 612 613 614 615 616
## 15.124164 13.572788 13.483286 12.890332 12.573345 14.288808 13.744335 13.569059
## 617 618 619 620 621 622 623 624
## 13.449722 12.416715 15.202478 11.715613 14.426791 15.019744 14.937700 13.490744
## 625 626 627 628 629 630 631 632
## 13.576518 14.061322 13.531766 14.493917 17.175261 14.240327 12.625554 14.091157
## 633 634 635 636 638 639 642 643
## 13.289364 14.672922 14.035217 13.311740 15.083142 14.225410 14.378310 12.666576
## 644 645 646 647 649 650 651 652
## 13.785357 13.852483 13.155110 13.662291 14.803447 13.572788 13.669749 12.293649
## 653 654 655 656 657 658 659 660
## 12.946271 13.841296 14.285078 14.810905 14.195576 11.734259 15.303169 12.591991
## 661 662 663 664 665 666 667 668
## 13.199862 14.117261 13.766710 12.662847 15.038391 13.483286 13.240883 12.950001
## 669 670 671 672 673 674 675 676
## 16.209381 13.211049 14.191847 12.972376 13.610081 14.173200 13.371408 14.374581
## 678 679 682 683 684 685 686 687
## 13.244613 13.792815 13.785357 13.222237 13.285635 13.494474 12.588262 11.868513
## 689 690 691 692 693 694 695 696
## 13.815191 11.663403 14.020300 13.804003 12.554698 14.352205 12.215335 13.997925
## 697 698 699 700 701 702 703 704
## 14.840739 12.841852 14.255244 13.624998 12.782184 14.001654 13.714500 13.725688
## 705 706 707 708 709 710 711 712
## 13.997925 13.509391 14.501376 13.542954 15.966978 13.375137 12.640471 13.341574
## 713 714 715 716 718 719 722 723
## 13.964361 13.621269 14.743778 13.971820 13.762981 14.568503 14.613254 13.170027
## 724 725 726 727 729 730 731 732
## 14.333559 13.830108 11.898347 13.412430 14.482730 14.094886 14.296266 12.051247
## 733 734 735 736 737 738 739 740
## 12.095998 15.098059 13.076796 13.132735 14.091157 12.916437 15.183832 17.622773
## 741 742 743 744 745 746 747 748
## 13.557871 14.382039 14.505105 12.461467 14.072510 14.613254 13.535496 12.051247
## 749 750 751 752 753 754 755 756
## 16.071398 15.579134 13.830108 13.680937 14.501376 13.647374 14.531210 13.755522
## 758 759 762 764 765 766 767 769
## 15.206208 13.908422 14.840739 14.203035 12.748620 13.591435 12.901520 14.296266
## 770 771 772 773 774 775 777 778
## 13.960632 13.043232 11.566442 13.211049 14.441708 12.726245 14.277620 12.498759
## 779 780 781 782 783 784 785 786
## 14.374581 13.453452 14.631900 14.180659 14.180659 13.751793 13.934527 14.855656
## 787 788 789 790 791 792 793 794
## 15.429964 13.542954 18.331334 14.266432 14.639359 13.531766 14.225410 15.370295
## 795 796 798 799 842 843 844 845
## 15.325544 13.423618 14.404415 14.937700 14.781071 13.591435 14.061322 16.131066
## 846 847 849 850 851 852 853 854
## 13.457181 12.923896 15.001098 14.027759 14.001654 13.789086 13.013398 14.602066
## 855 857 859 860 861 862 863 864
## 14.083698 14.874303 15.843912 13.274447 13.337844 14.870573 14.531210 14.098615
## 865 866 867 868 869 870 871 872
## 13.695854 14.337288 14.456625 14.471542 16.802334 14.527481 14.046405 13.804003
## 873 874 875 876 878 879
## 14.557315 13.762981 14.672922 14.363393 14.437978 14.564774morph_res <- residuals(morph_mod) #extracts residuals of model
morph_res## 1 2 3 4 5 6
## 0.511386306 -0.011540465 0.308181408 -0.060850236 0.201444986 -0.476430741
## 7 8 9 10 11 12
## -0.135157463 0.705169163 0.263927771 0.110808347 -0.488640489 0.995998455
## 13 14 15 16 17 18
## -0.013835687 -0.998501425 -0.229747907 0.707218143 -0.019330717 0.352820352
## 19 20 21 22 23 24
## -0.104081929 1.506025250 0.006800952 0.507523065 -0.107896671 -0.408945410
## 25 26 27 28 29 30
## 1.014398551 -0.074028340 0.272130124 -0.625794102 0.901776702 0.488705778
## 31 32 33 34 35 36
## 0.224896126 -0.441016095 0.662049740 0.463071684 -0.009303922 -0.032701473
## 37 38 39 40 41 42
## 0.167079079 -0.447591749 -0.072342962 -0.394360056 1.072103329 0.631193653
## 43 44 45 46 47 48
## 0.155227843 -0.509994150 0.481054590 -2.913530765 -0.128111029 0.592600904
## 49 50 51 52 53 54
## -0.025986755 1.058127819 0.990722873 0.184291372 -0.033916071 2.791022705
## 55 56 57 58 59 60
## -0.124857631 0.195949956 -0.751289132 -0.016018640 -0.628720873 0.053735118
## 61 62 63 64 65 66
## -0.064220993 -0.415708628 -0.506430741 0.081937471 0.022991300 -0.816045434
## 67 68 69 70 71 72
## 0.831054590 -0.054001545 0.721776702 0.517159463 -0.350240393 0.336940016
## 73 74 75 76 77 78
## 0.888127819 -0.283391701 -0.280020945 0.552049740 -0.164440441 -0.921786707
## 79 81 82 83 84 85
## 2.910391156 -1.116511125 0.011225538 -0.376896431 -0.444215903 -1.057030405
## 86 87 88 89 90 91
## -0.101315927 -0.182530525 0.545944866 0.406886426 0.765645034 -0.424879336
## 92 93 94 95 96 97
## -0.671925771 0.295837687 -0.362696383 1.482852237 0.394237783 -0.961123274
## 98 99 100 101 102 103
## -1.245242938 -1.683632854 1.477271732 -0.396372061 -0.409213358 -3.045366731
## 104 105 106 107 108 109
## -0.526067139 -0.208555014 0.158764457 -0.106206203 0.176308467 -0.264435351
## 110 111 112 113 114 115
## 0.221471780 -0.977281737 -1.157474390 0.442354662 0.110257182 0.381723113
## 116 117 118 119 121 122
## -0.368720873 -0.547725723 -0.790042650 -1.701647644 0.602713173 -0.677474390
## 123 124 125 126 127 128
## 1.339871876 -0.690486635 -0.837137584 0.233906066 -0.970952325 1.028957110
## 129 130 131 132 133 134
## -0.632942626 -0.351588964 -1.077335327 0.727330412 0.312413341 0.210150004
## 135 136 137 138 139 140
## 0.656859631 -0.464184018 -0.561893886 0.241418191 0.507442681 -3.269283562
## 141 142 143 144 145 146
## -2.307608364 -0.526035255 -0.774050044 -1.877527980 0.164071924 -0.307394006
## 147 148 149 150 151 152
## -1.008662193 -0.467362121 -0.362166923 -0.822172013 -0.729047500 -1.174547620
## 153 154 155 156 157 158
## -1.158854846 -1.410540225 -0.074628004 0.092359751 -0.991647644 -0.601423106
## 159 162 163 164 165 166
## 1.090615694 -0.688796167 0.348271972 0.542605994 0.217035670 0.675923161
## 167 169 170 171 172 173
## -0.399844907 -0.934901041 -0.989957175 -0.391754822 0.032857326 -1.566976815
## 174 175 176 177 178 179
## -0.432584114 -0.068137824 -0.030396071 0.620759847 1.155366906 -0.348962025
## 180 181 182 183 184 185
## 1.676501120 -0.577940081 -1.592852062 -0.062525435 -0.838603514 1.023440376
## 186 187 188 189 190 191
## -0.797720633 0.453269427 -0.220010765 -0.600866851 -0.652086539 -0.497362121
## 192 193 194 195 196 197
## -1.390866851 -2.457110789 -0.457913286 1.126228083 -0.274847452 -0.240288892
## 198 199 202 203 204 205
## -1.544847452 -1.402552230 -1.322552230 -1.600620609 0.009213533 -0.962135039
## 206 207 209 210 211 212
## 0.484184193 -0.298903346 -0.770369276 -0.086944931 -0.386725483 0.549293917
## 213 214 215 216 217 218
## -0.456340177 -0.729818112 1.657935166 -0.213569084 1.075981840 0.457662128
## 219 220 221 222 223 224
## -0.335093694 0.417223233 -1.271364426 -2.113349637 0.620401336 -0.782691293
## 225 226 227 228 229 230
## 1.316286762 0.160979295 -0.854098544 0.080540400 -0.939898496 0.871230628
## 231 232 233 234 235 236
## 0.365537855 -0.802220513 -0.136420561 0.397255117 0.213001480 0.788576894
## 238 239 242 243 244 245
## -0.748245003 -1.415147284 -0.048571629 -0.577469300 -1.445725243 0.963696798
## 246 247 249 250 251 252
## 1.076479415 -0.686276407 -0.350283802 -0.829508100 -0.482466755 -0.080235303
## 253 254 255 256 257 258
## 0.188052524 -0.061225363 1.169128059 0.844906306 0.875264817 -0.037720633
## 259 260 261 262 263 264
## 0.203830772 -1.222386371 -0.012691293 -2.095720153 0.891037975 -1.222413166
## 265 266 267 268 269 270
## 2.827891756 -0.248822962 0.836698863 0.021342897 -0.495864306 0.428635574
## 271 272 273 274 275 276
## 0.371754997 -0.335313142 0.250181888 -0.165976575 0.007725898 -0.686420561
## 278 279 282 283 284 285
## -2.263900801 -3.636469060 -0.608293502 -1.615452206 0.726757542 -0.280803082
## 286 287 289 290 291 292
## -3.639524715 -2.878491245 -1.616886251 -1.363788532 -1.701359336 0.572776942
## 293 294 295 296 297 298
## -0.442969420 0.266784337 0.547250027 -1.397764042 0.299245417 0.361701408
## 299 300 301 302 303 304
## 0.716730748 0.258662368 -0.884125339 -0.520417776 -1.696661713 -0.823242458
## 305 306 307 308 309 310
## 2.030074709 0.998721048 -1.599705843 0.600374541 -0.624093454 -0.766308292
## 311 312 313 314 315 316
## -1.266527740 0.187089259 -0.265366731 1.237394181 -0.950144739 -1.338710693
## 318 319 322 323 324 325
## -1.678705603 -2.748095759 -0.167988580 -1.134510645 -1.022381281 0.650967770
## 326 327 329 330 331 332
## 0.641540640 -2.338454271 -0.606222818 0.434306642 -1.813761737 0.503359991
## 333 334 335 336 337 338
## -0.290700993 -1.228320297 0.922611084 -0.682820177 0.916928491 0.110181888
## 339 340 341 342 343 344
## -4.408127644 -1.456303202 -0.360834967 0.257484745 0.479357686 -0.696966635
## 345 346 347 348 349 350
## -1.399171293 0.818860111 0.487672308 0.049716198 -1.396271317 -1.615944691
## 351 352 353 354 355 356
## -0.536196023 0.116703953 -0.719369036 -0.599834727 1.681289307 0.263140544
## 358 359 362 363 364 365
## -1.683344547 -1.235554295 -2.387100609 2.207469475 0.140021120 -0.740910261
## 366 367 369 370 371 372
## 0.081460255 0.445414061 -2.357876311 -0.694585939 -4.192371101 -0.707383826
## 373 374 375 376 377 378
## -0.227025315 0.459138239 3.077415886 0.318453100 0.724879511 -0.046388676
## 379 380 381 382 383 384
## -0.377790837 -0.796827572 0.552979775 -0.548149349 0.343172428 -0.176217728
## 385 386 387 388 389 390
## 0.155387266 1.016682248 -0.213403226 0.391021360 -0.461434631 0.681679703
## 391 392 393 394 395 396
## -1.037929901 -1.118400681 -1.580530045 1.204943280 0.089582224 -1.858785987
## 398 399 402 403 404 405
## -0.168288412 -1.384944451 -2.326656624 -1.454810477 -0.447212878 0.149175213
## 406 407 409 410 411 412
## 0.311626114 -0.609390741 -1.557485915 0.739528635 -2.167432326 1.186623569
## 413 414 415 416 417 418
## -3.992188628 0.550465105 -0.377742338 -0.704088364 1.744884601 -0.050117944
## 419 420 421 422 423 424
## -2.686378496 -0.294810477 -1.213563994 0.363343376 -0.227651774 -2.478646924
## 425 426 427 428 429 430
## 1.352182368 0.204087194 0.933338287 -1.984061570 -2.249246588 -0.221049325
## 431 432 433 434 435 436
## -0.332349397 -0.958893166 -0.543729853 -1.652483370 -1.334002890 -1.315607884
## 438 439 442 443 444 445
## -0.908534655 -1.237678568 -1.226876071 -0.911851822 -1.294671413 -0.607341762
## 446 447 449 450 451 452
## -0.478229733 -1.859497920 -0.448507860 0.443423761 -0.564141954 0.417233413
## 453 454 455 456 457 458
## 0.874028515 -2.632900561 -0.166303202 0.359202008 1.440411516 1.306569979
## 459 460 461 462 463 464
## 0.355858046 2.040738143 -1.221188388 0.217463040 -0.828261618 -2.015302962
## 465 466 467 468 469 470
## -1.248727308 -0.427015135 1.365023665 -0.865912806 -1.087946516 -0.484473670
## 471 472 473 474 475 476
## -0.122290717 0.005109139 1.337292092 -0.221049325 0.015826162 0.354418911
## 478 479 482 483 484 485
## -0.299722458 -0.996544355 -1.389171293 0.992562584 -0.131241978 1.793621504
## 486 487 489 490 491 492
## 1.252872596 -0.080632134 0.090004505 0.056243352 -2.516902866 1.105243112
## 493 494 495 496 497 498
## -0.207405531 -0.354998040 1.474001720 -0.378144259 0.388148178 -0.404617824
## 499 500 501 502 503 504
## -2.212590549 -1.071081209 -1.626271317 -0.913585699 0.287377566 -2.148342002
## 505 506 507 508 509 510
## -0.138063875 -1.254612734 -1.985581089 -0.196324907 -2.630653839 0.064006810
## 511 512 513 514 515 516
## 0.440523785 -2.987871221 0.288479895 -0.620963851 -0.024056480 0.182348226
## 518 519 522 523 524 525
## -1.340685723 -0.319417536 -0.825656384 -0.264366491 -0.309556600 0.713846041
## 526 527 529 530 531 532
## -0.023837032 0.694311732 -0.827812542 -0.472729613 -0.404168748 -0.572873766
## 533 534 535 536 537 538
## 0.125606714 -0.346956456 -1.664366491 0.918319127 0.915060639 1.138009115
## 539 540 541 542 543 544
## -1.004356312 -0.648866371 -1.469722458 -1.182922266 -0.564110069 -1.856458881
## 545 546 547 548 549 550
## 1.057265297 -0.679690573 0.757350771 1.214862896 0.831256077 0.734397206
## 551 552 553 554 555 556
## -0.460134559 0.912021600 -1.607732158 -0.122702818 -0.422975855 -1.495490525
## 558 559 562 563 564 565
## -2.951322362 0.114782512 -1.041210093 -1.963590789 -1.153366252 2.721272692
## 566 567 569 570 571 572
## 0.244450795 0.450363016 -1.161402746 2.485221408 -0.936988340 -0.476768892
## 573 574 575 576 577 578
## 1.420411516 -1.220905171 -0.411600489 1.767709283 -0.021985795 -0.470829877
## 579 580 581 582 583 584
## -0.938722218 -0.222980945 0.215274997 1.741304577 0.580416606 1.036628659
## 585 586 587 588 589 590
## 2.400443400 -1.689856432 1.179202008 1.177350771 0.015151203 -1.964024595
## 591 592 593 594 595 596
## 0.466992260 0.598650843 0.340336221 -2.060493070 1.502433700 0.703867746
## 598 599 602 603 604 605
## 0.573680183 -0.173612494 -0.829192998 -0.347983490 -0.041654079 0.566911876
## 606 607 609 610 611 612
## 0.236606954 0.140999655 -1.904163659 1.457211708 0.576714133 0.189667698
## 613 614 615 616 617 618
## -0.653344547 -2.718807692 0.955665393 1.670940975 1.970277542 2.383284697
## 619 620 621 622 623 624
## 0.557521720 1.054387026 -1.576790597 -0.199744163 0.072299727 -1.630744403
## 625 626 627 628 629 630
## 1.303482440 -0.881322362 1.038233653 0.266082584 -0.855260898 1.469672788
## 631 632 633 634 635 636
## 1.664445705 -0.501156504 0.040636053 -1.982922266 1.264782512 -0.391739553
## 638 639 642 643 644 645
## -0.003141714 -0.365410141 -0.698310117 1.743423761 -0.115356552 2.047516630
## 646 647 649 650 651 652
## 1.454889691 -0.582290717 -2.853446636 0.807211708 -2.449749253 1.646350531
## 653 654 655 656 657 658
## 1.523728683 -1.661295567 -1.265078424 0.189094829 0.994424001 2.345740688
## 659 660 661 662 663 664
## -1.293168509 -0.421990885 0.540138478 1.452738622 0.713289787 2.877153028
## 665 666 667 668 669 670
## -0.188390501 1.556714133 1.479116534 1.129999415 -0.699380561 3.078950675
## 671 672 673 674 675 676
## 2.568153268 0.767623809 0.489919031 1.446799607 2.648592164 1.225419151
## 678 679 682 683 684 685
## 1.975387266 2.447184913 0.684643448 -0.692237128 -0.565634679 1.805526330
## 686 687 689 690 691 692
## -0.038261618 2.301487050 -1.855190693 0.636596774 -0.370300417 0.795997110
## 693 694 695 696 697 698
## 1.055301792 -2.092205243 1.514665153 1.492075189 -0.680739313 -1.401851822
## 699 700 701 702 703 704
## 0.904755717 -0.264998040 1.527816462 0.408345921 -0.804500465 -0.805688268
## 705 706 707 708 709 710
## 1.002075189 0.090609259 1.348624049 -0.152954151 0.453021840 2.034862896
## 711 712 713 714 715 716
## 2.919528635 0.708426306 1.035638598 3.058731228 -0.723778352 0.888180063
## 718 719 722 723 724 725
## -0.032980945 -0.628502770 -0.773253983 1.149972620 -1.273558905 1.559892236
## 726 727 729 730 731 732
## 0.801652908 1.717570219 0.697270387 0.805114229 -1.656266228 0.778752932
## 733 734 735 736 737 738
## 2.834001720 -1.018058785 0.063204313 1.737265297 2.068843496 0.163562824
## 739 740 741 742 743 744
## -0.693831942 -2.172773023 0.042128779 1.887960615 -0.385105219 2.568533485
## 745 746 747 748 749 750
## 2.127489835 -2.103253983 1.214504385 1.608752932 -0.371397656 1.250865681
## 751 752 753 754 755 756
## 0.619892236 0.599062944 -2.051375951 2.422626354 3.138789907 0.794477590
## 758 759 762 764 765 766
## -1.046207548 1.971577614 -0.540739313 0.606965465 2.971379871 2.428565369
## 767 769 770 771 772 773
## 1.628479895 1.963733772 1.039367866 0.946767722 1.693557734 1.678950675
## 774 775 777 778 779 780
## -0.471707668 2.033755477 2.542380111 0.171240807 0.915419151 2.196548274
## 781 782 783 784 785 786
## -0.681900321 1.779341071 2.229341071 2.088206858 3.365472740 -0.635656384
## 787 788 789 790 791 792
## -2.209963611 1.877045849 -3.181333887 2.233567914 1.150641143 -0.411766347
## 793 794 795 796 798 799
## 0.514589859 -0.470295327 0.824455885 0.796382416 1.465585009 0.052299727
## 842 843 844 845 846 847
## 1.388928971 1.608565369 -0.741322362 0.518934060 2.842819007 2.306104289
## 849 850 851 852 853 854
## 1.618902176 1.632241047 -0.551654079 0.700914181 3.376601864 -0.272066180
## 855 857 859 860 861 862
## 2.606302032 0.345697278 0.226087674 2.095553124 2.422155573 1.429426546
## 863 864 865 866 867 868
## 0.568789907 1.731384961 3.024145873 1.072711828 1.763375261 0.238458190
## 869 870 871 872 873 874
## 1.337665873 1.062519175 1.993594709 1.955997110 -0.777314967 3.597019055
## 875 876 878 879
## 0.477077734 2.616606954 2.002021600 0.165226498qplot(morph_fit, morph_res) #plot relationship of predicted vs residuals of model see no relationship 
qqnorm(morph_res)
qqline(morph_res)
plot(profile(morph_mod)) #must see a line and then we're okay (splits the V) 
#LRT test of model
morph_mod_null <- glm(culmen_mm ~ 1, #what would response var would look like in a null situation (~1)
family = gaussian(link = "identity"),
data=morphology)
anova(morph_mod_null, morph_mod, test = "LRT") #like ratio test #look p-value and so reject the null ## Analysis of Deviance Table
##
## Model 1: culmen_mm ~ 1
## Model 2: culmen_mm ~ tarsus_mm
## Resid. Df Resid. Dev Df Deviance Pr(>Chi)
## 1 765 6000.9
## 2 764 1171.7 1 4829.3 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#t-tests of parameters
summary(morph_mod)##
## Call:
## glm(formula = culmen_mm ~ tarsus_mm, family = gaussian(link = "identity"),
## data = morphology)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.4081 -0.7029 -0.0328 0.7263 3.5970
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.098707 0.215450 -0.458 0.647
## tarsus_mm 0.372927 0.006646 56.116 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 1.533593)
##
## Null deviance: 6000.9 on 765 degrees of freedom
## Residual deviance: 1171.7 on 764 degrees of freedom
## AIC: 2505.4
##
## Number of Fisher Scoring iterations: 2#BAYESIAN####
morph_lm_bayes <- brm(culmen_mm ~ tarsus_mm, #create bayes model (y~x)
family = gaussian(link="identity"),
data= morphology)## Compiling Stan program...## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
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## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
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## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
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## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
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## Chain 4:morph_lm_bayes## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: culmen_mm ~ tarsus_mm
## Data: morphology (Number of observations: 766)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.10 0.22 -0.53 0.34 1.00 4803 3056
## tarsus_mm 0.37 0.01 0.36 0.39 1.00 4841 3004
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.24 0.03 1.18 1.30 1.00 3599 2891
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).print(summary(morph_lm_bayes), digits= 5) #summary table with 5 digits out## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: culmen_mm ~ tarsus_mm
## Data: morphology (Number of observations: 766)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.09660 0.21934 -0.53210 0.33794 1.00033 4803 3056
## tarsus_mm 0.37285 0.00679 0.35953 0.38632 1.00024 4841 3004
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.24106 0.03176 1.18081 1.30492 1.00232 3599 2891
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).color_scheme_set("viridis") #set a color scheme
#visually investigate our chains
#chains converge priors look great!
plot(morph_lm_bayes) 
plot(morph_lm_bayes, par= "b_Intercept")
mcmc_trace(morph_lm_bayes)
#Look at a diagnostic of convergence
#Gelmen-Rubin statistic-- Rhat (want Rhat to be 1)
rhat(morph_lm_bayes) #can see all values are close to 1 #looks good!## b_Intercept b_tarsus_mm sigma lp__
## 1.0003220 1.0002465 0.9997096 1.0014244 #usually only work if off by something in the hundredths
mcmc_acf(morph_lm_bayes) #looks good
#check the match between our data and our chains
# for distributions of data of y
pp_check(morph_lm_bayes, "dens_overlay") #green is posteriors from fit## Using 10 posterior samples for ppc type 'dens_overlay' by default.
#black is dist of length in bayes
#looks like a good fit!
#is our error normal? checking our residuals
#about error and future predictions
pp_check(morph_lm_bayes, "error_hist") #residuals look good!## Using 10 posterior samples for ppc type 'error_hist' by default.## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
pp_check(morph_lm_bayes, "error_scatter") #relationship ## Using 10 posterior samples for ppc type 'error_scatter' by default.
#between residuals and obs values.. see that it's
#generally linear so we're good!
pp_check(morph_lm_bayes, "error_scatter_avg") #takes avg pred error## Using all posterior samples for ppc type 'error_scatter_avg' by default.
#over all posteriors
#to get at looking at fitted v residuals. did we miss a nonlinearity??
morph_res <- residuals(morph_lm_bayes) %>%
as_tibble
morph_fit <- fitted(morph_lm_bayes) %>%
as_tibble
plot(y=morph_res$Estimate, x=morph_fit$Estimate) #fitted vs res plot. All looks good!
5b) Three interpretations (10 points) OK, now that we have fits, take a look! Do the coefficients and their associated measures of error in their estimation match? How would we interpret the results from these different analyses differently? Or would we? Note, confint works on lm objects as well.
We see that our lm and glm models produce the exact same coefficients and the associated measures of error, bayes produces nearly the same coeff/err. We wouldn’t interpret the lm/glm results differently. Bayes is slightly diff b/c it’s asking a diff question and performing a different function but b/c we didn’t input priors into the function this is why we get nearly the same outputs. I would argue b/c we aren’t using any priors a lm or glm will work to answer the question being asked: Is there a relationship between Tarsus and culmun? Can we use tarsus length to predict culmun?
One other aspect to look at is the confidence intervals vs credible intervals. The glm and lm both have very similar confidence intervals which tells us how confident we are that our values are truly apart of this model. And if we wanted to replicate this experiment again, our true value would occur 95% percent of the time. In the bayes analysis though, we are looking at credible intervals which tell us the area that we will find 95% of our possible parameter values.
LM Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.098707 0.215450 -0.458 0.647
tarsus_mm 0.372927 0.006646 56.116 <2e-16 *** 2.5 % 97.5 % (Intercept) -0.5216505 0.3242363 tarsus_mm 0.3598809 0.3859727
GLM Coefficients: Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.098707 0.215450 -0.458 0.647
tarsus_mm 0.372927 0.006646 56.116 <2e-16 ***
2.5 % 97.5 %(Intercept) -0.5209805 0.3235663 tarsus_mm 0.3599015 0.3859520
BRM Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Intercept -0.09415 0.21423 -0.51603 0.32000 1.00038 4491 tarsus_mm 0.37278 0.00661 0.35975 0.38575 1.00037 4511 Tail_ESS Intercept 3111 tarsus_mm 3105
#summary of models
summary(lm_morph)##
## Call:
## lm(formula = culmen_mm ~ tarsus_mm, data = morphology)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.4081 -0.7029 -0.0328 0.7263 3.5970
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.098707 0.215450 -0.458 0.647
## tarsus_mm 0.372927 0.006646 56.116 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.238 on 764 degrees of freedom
## Multiple R-squared: 0.8048, Adjusted R-squared: 0.8045
## F-statistic: 3149 on 1 and 764 DF, p-value: < 2.2e-16summary(morph_mod)##
## Call:
## glm(formula = culmen_mm ~ tarsus_mm, family = gaussian(link = "identity"),
## data = morphology)
##
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -4.4081 -0.7029 -0.0328 0.7263 3.5970
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.098707 0.215450 -0.458 0.647
## tarsus_mm 0.372927 0.006646 56.116 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## (Dispersion parameter for gaussian family taken to be 1.533593)
##
## Null deviance: 6000.9 on 765 degrees of freedom
## Residual deviance: 1171.7 on 764 degrees of freedom
## AIC: 2505.4
##
## Number of Fisher Scoring iterations: 2print(summary(morph_lm_bayes), digits= 5) #summary table with 5 digits out## Family: gaussian
## Links: mu = identity; sigma = identity
## Formula: culmen_mm ~ tarsus_mm
## Data: morphology (Number of observations: 766)
## Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
## total post-warmup samples = 4000
##
## Population-Level Effects:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## Intercept -0.09660 0.21934 -0.53210 0.33794 1.00033 4803 3056
## tarsus_mm 0.37285 0.00679 0.35953 0.38632 1.00024 4841 3004
##
## Family Specific Parameters:
## Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
## sigma 1.24106 0.03176 1.18081 1.30492 1.00232 3599 2891
##
## Samples were drawn using sampling(NUTS). For each parameter, Bulk_ESS
## and Tail_ESS are effective sample size measures, and Rhat is the potential
## scale reduction factor on split chains (at convergence, Rhat = 1).#conf intervals for each model
confint(morph_mod) ## Waiting for profiling to be done...## 2.5 % 97.5 %
## (Intercept) -0.5209805 0.3235663
## tarsus_mm 0.3599015 0.3859520confint(lm_morph)## 2.5 % 97.5 %
## (Intercept) -0.5216505 0.3242363
## tarsus_mm 0.3598809 0.38597275c) Everyday I’m Profilin’ (10 points) For your likelihood fit, are your profiles well behaved? For just the slope, use grid sampling to create a profile. You’ll need to write functions for this, sampling the whole grid of slope and intercept, and then take out the relevant slices as we have done before. Use the results from the fit above to provide the reasonable bounds of what you should be profiling over (3SE should do). Is it well behaved? Plot the profile and give the 80% and 95% CI (remember how we use the chisq here!). Verify your results with profileModel.
Our profiles seem to be well behaved behaved. Our plot and ProfileModel plot both give us nice parabolic curves.
95% CI is slopes 0.3706061 - 0.3722222 80% CI is slopes 0.3710101 - 0.3718182
#write a function sampling the whole grid of slope and intercept, and then take out the relevant slices as we have done before
likhood_fun <- function(slope, intercept){ #function given slope/int
morph_new <- slope* morphology$tarsus_mm + intercept
#creating data set that includes operation for linear regression
sum(dnorm(morphology$culmen_mm, morph_new, log = TRUE)) #sum all the log data
}
morph_grid <- tibble(slope = seq(0.35, 0.39, length.out = 100), #create tibble that seq over 3SE of our slope and intercept values found from 5b
intercept = seq(-0.74, 0.55, length.out= 100)) %>%
group_by(slope, intercept) %>% #group by slope and int
mutate(loglikelihood = likhood_fun(slope,intercept), #put our slope/int through likhood function and set deviance to measure our fit
deviance = -2 * loglikelihood) %>%
ungroup()
like_plot <- ggplot(data=morph_grid, #plot our data to look at slope and the loglikelihood of these sloeps
mapping=aes(x=slope,
y=loglikelihood)) +
geom_point()+
geom_line(data= morph_grid%>% #create ranges of where our slope is within 95% CI. #'s grabbed from here to also put the range of our slopes in answer above
filter(loglikelihood >= (max(loglikelihood)- qchisq(0.95, df=1)/2)) %>%
as.data.frame()%>%
head(),
aes(x=slope,
y=loglikelihood),
color="pink",
size=4)+
geom_line(data= morph_grid %>% #create ranges of where our slope is within 80% CI. #'s grabbed from here to also put the range of our slopes in answer above
filter(loglikelihood >= (max(loglikelihood)- qchisq(0.80, df=1)/2)),
aes(x=slope,
y=loglikelihood),
color="blue",
size=4)
#check with profileModel and I'd say our model is well behaved.This is our deviance profile and it shows us nice parabolic curved shapes
morph_prof_model <- profileModel(morph_mod,
objective = "ordinaryDeviance",
quantile = qchisq(0.8,0.95))## Preliminary iteration .. Done
##
## Profiling for parameter (Intercept) ... Done
## Profiling for parameter tarsus_mm ... Doneplot(morph_prof_model)
5d) The Power of the Prior (10 points) This data set is pretty big. After excluding NAs in the variables we’re interested in, it’s over 766 lines of data! Now, a lot of data can overwhelm a strong prior. But only to a point. Show first that there is enough data here that a prior for the slope with an estimate of 0.7 and a sd of 0.01 is overwhelmed and produces similar results to the default prior. How different are the results from the original? Second, randomly sample 10, 100, 300, and 500 data points. At which level is our prior overwhelmed (e.g., the prior slope becomes highly unlikely)? Communicate that visually in the best way you feel gets the point across, and explain your reasoning.
Old vs new we see that there is a quite a difference in our y-intercept and also a difference in our slope. It makes sense though that we have a slight shift toward a 0.7 slope since we put that in as a prior our y-int is really different though! When we start to change our sample size though we see that a larger sample size (over 10) overwhelms our prior. We would expect this to happen and I’d argue 10 doesn’t overwhelm it b/c there is a good amount of overlap between that and our origonal. Once we look at the n=100 though only a small part of the tail maybe overlaps with the origonal. But again this makes sense b/c 10 samples is very different than 100!
BRM- old Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Intercept -0.09415 0.21423 -0.51603 0.32000 1.00038 4491 tarsus_mm 0.37278 0.00661 0.35975 0.38575 1.00037 4511
BRM- new Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS Intercept -4.25 0.27 -4.78 -3.72 1.00 1980 2072 tarsus_mm 0.50 0.01 0.49 0.52 1.00 1925 2069
#set up strong prior
morph_lm_bayes <- brm(culmen_mm ~ tarsus_mm, #create bayes model (y~x)
family = gaussian(link="identity"),
data= morphology%>%
sample_n(10),
#prior for the slope
prior = c(prior(coef = "tarsus_mm",
#with an estimate of 0.7 (mean) and sd of 0.01
prior = normal(0.7,0.01))),
chains = 3)## Compiling Stan program...## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
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## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
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## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL '82ea377065a124f0e1eacafbba221e5e' NOW (CHAIN 1).
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## Chain 1:
##
## SAMPLING FOR MODEL '82ea377065a124f0e1eacafbba221e5e' NOW (CHAIN 2).
## Chain 2:
## Chain 2: Gradient evaluation took 1e-05 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.1 seconds.
## Chain 2: Adjust your expectations accordingly!
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## Chain 2:
##
## SAMPLING FOR MODEL '82ea377065a124f0e1eacafbba221e5e' NOW (CHAIN 3).
## Chain 3:
## Chain 3: Gradient evaluation took 9e-06 seconds
## Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.
## Chain 3: Adjust your expectations accordingly!
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## Chain 3:#randomly sample 10 data points, put sample n=10 to only pull 10 random draws from our morph data
morph_lm_bayes_10 <- brm(culmen_mm ~ tarsus_mm, #create bayes model (y~x)
family = gaussian(link="identity"),
data= morphology%>%
sample_n(10),
#prior for the slope
prior = c(prior(coef = "tarsus_mm",
#with an estimate of 0.7 (mean) and sd of 0.01
prior = normal(0.7,0.01))),
chains = 3)## Compiling Stan program...
## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL 'dafad7e2c339b2b81ac6f30b057e8a92' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 1.9e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds.
## Chain 1: Adjust your expectations accordingly!
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## Chain 1: 0.048973 seconds (Total)
## Chain 1:
##
## SAMPLING FOR MODEL 'dafad7e2c339b2b81ac6f30b057e8a92' NOW (CHAIN 2).
## Chain 2:
## Chain 2: Gradient evaluation took 8e-06 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.
## Chain 2: Adjust your expectations accordingly!
## Chain 2:
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## Chain 2:
##
## SAMPLING FOR MODEL 'dafad7e2c339b2b81ac6f30b057e8a92' NOW (CHAIN 3).
## Chain 3:
## Chain 3: Gradient evaluation took 1.7e-05 seconds
## Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds.
## Chain 3: Adjust your expectations accordingly!
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## Chain 3:#randomly sample 100 data points put sample n=100 to only pull 100 random draws from our morph data
morph_lm_bayes_100 <- brm(culmen_mm ~ tarsus_mm, #create bayes model (y~x)
family = gaussian(link="identity"),
data= morphology%>%
sample_n(100),
#prior for the slope
prior = c(prior(coef = "tarsus_mm",
#with an estimate of 0.7 (mean) and sd of 0.01
prior = normal(0.7,0.01))),
chains = 3)## Compiling Stan program...
## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL 'e06e4b78b9092964909aba153e1b2b2c' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 2.4e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
## Chain 1: Adjust your expectations accordingly!
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## Chain 1: 0.039498 seconds (Total)
## Chain 1:
##
## SAMPLING FOR MODEL 'e06e4b78b9092964909aba153e1b2b2c' NOW (CHAIN 2).
## Chain 2:
## Chain 2: Gradient evaluation took 1.3e-05 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.13 seconds.
## Chain 2: Adjust your expectations accordingly!
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## Chain 2:
##
## SAMPLING FOR MODEL 'e06e4b78b9092964909aba153e1b2b2c' NOW (CHAIN 3).
## Chain 3:
## Chain 3: Gradient evaluation took 9e-06 seconds
## Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.
## Chain 3: Adjust your expectations accordingly!
## Chain 3:
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## Chain 3: 0.035241 seconds (Total)
## Chain 3:#randomly sample 300 data points put sample n=300 to only pull 300 random draws from our morph data
morph_lm_bayes_300 <- brm(culmen_mm ~ tarsus_mm, #create bayes model (y~x)
family = gaussian(link="identity"),
data= morphology%>%
sample_n(300),
#prior for the slope
prior = c(prior(coef = "tarsus_mm",
#with an estimate of 0.7 (mean) and sd of 0.01
prior = normal(0.7,0.01))),
chains = 3)## Compiling Stan program...
## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL 'd6c67efac8a583b096d2bf215fb63706' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 2.1e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.21 seconds.
## Chain 1: Adjust your expectations accordingly!
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## Chain 1:
## Chain 1: Elapsed Time: 0.023759 seconds (Warm-up)
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## Chain 1: 0.046474 seconds (Total)
## Chain 1:
##
## SAMPLING FOR MODEL 'd6c67efac8a583b096d2bf215fb63706' NOW (CHAIN 2).
## Chain 2:
## Chain 2: Gradient evaluation took 1.1e-05 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.
## Chain 2: Adjust your expectations accordingly!
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## Chain 2:
## Chain 2: Elapsed Time: 0.02499 seconds (Warm-up)
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## Chain 2: 0.046017 seconds (Total)
## Chain 2:
##
## SAMPLING FOR MODEL 'd6c67efac8a583b096d2bf215fb63706' NOW (CHAIN 3).
## Chain 3:
## Chain 3: Gradient evaluation took 2e-05 seconds
## Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.2 seconds.
## Chain 3: Adjust your expectations accordingly!
## Chain 3:
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## Chain 3:
## Chain 3: Elapsed Time: 0.030612 seconds (Warm-up)
## Chain 3: 0.021395 seconds (Sampling)
## Chain 3: 0.052007 seconds (Total)
## Chain 3:#randomly sample 500 data points put sample n=500 to only pull 500 random draws from our morph data
morph_lm_bayes_500 <- brm(culmen_mm ~ tarsus_mm, #create bayes model (y~x)
family = gaussian(link="identity"),
data= morphology%>%
sample_n(500),
#prior for the slope
prior = c(prior(coef = "tarsus_mm",
#with an estimate of 0.7 (mean) and sd of 0.01
prior = normal(0.7,0.01))),
chains = 3)## Compiling Stan program...
## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL 'c3862f0336279ab33ad03942a6f73591' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 2.3e-05 seconds
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## SAMPLING FOR MODEL 'c3862f0336279ab33ad03942a6f73591' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'c3862f0336279ab33ad03942a6f73591' NOW (CHAIN 3).
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## Chain 3:#set them all as df
morph_lm_bayes <- as.data.frame(morph_lm_bayes)
morph_lm_bayes_10 <- as.data.frame(morph_lm_bayes_10)
morph_lm_bayes_100 <- as.data.frame(morph_lm_bayes_100)
morph_lm_bayes_300 <- as.data.frame(morph_lm_bayes_300)
morph_lm_bayes_500 <- as.data.frame(morph_lm_bayes_500)
ggplot()+ #plot all of our different samples to visualize. The black fill is our actual prior
geom_density(data = morph_lm_bayes,
mapping = aes(x=b_tarsus_mm),
alpha=0.2, fill="black") +
geom_density(data = morph_lm_bayes_10,
mapping = aes(x=b_tarsus_mm),
alpha=0.2, color="purple") +
geom_density(data = morph_lm_bayes_100,
mapping = aes(x=b_tarsus_mm),
alpha=0.2, color="orange") +
geom_density(data = morph_lm_bayes_300,
mapping = aes(x=b_tarsus_mm),
alpha=0.2, color="red") +
geom_density(data = morph_lm_bayes_500,
mapping = aes(x=b_tarsus_mm),
alpha=0.2, color="yellow")
- Cross-Validation and Priors (15 points) There is some interesting curvature in the culmen-tarsus relationship. Is the relationship really linear? Squared? Cubic? Exponential? Use one of the cross-validation techniques we explored to show which model is more predictive. Justify your choice of technique. Do you get a clear answer? What does it say?
It seems that our relationship between culmen and tarsus is cubic as predicted by both Kfold and LOO models. We got a clear answer from our tibble outputs when comparing polys b/c of zero values for the cubic model. Although we did run both cross-val techniques, in the future I would say that running just Kfold would have worked best b/c our data set is large. When doing leave one out cross val this is technically used for smaller data sets b/c it only pulls one data point out each time which helps to keep each sample size big. Our data set is large though so this isn’t really something we need to worry about.
KFOLD elpd_diff se_diff morph_cub 0.0 0.0 morph_four -2.6 1.3 morph_lm -12.9 5.1 morph_sq -14.2 5.5 morph_int -638.5 23.7
LOO elpd_diff se_diff morph_cub 0.0 0.0 morph_four -0.9 0.3 morph_lm -12.1 5.3 morph_sq -13.2 5.6 morph_int -636.5 23.7
#set up our polys to compare####
morph_lm <- brm(culmen_mm~tarsus_mm,
data=morphology,
family= gaussian(link="identity"))## Compiling Stan program...## recompiling to avoid crashing R session## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 1).
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## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 2).
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## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 3).
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## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 4).
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## Chain 4:morph_int <- brm(culmen_mm~1,
data=morphology,
family= gaussian(link="identity")) ## Compiling Stan program...
## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL '44e07d1ba7fab7a41d9b7e567b76929b' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 3.7e-05 seconds
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## SAMPLING FOR MODEL '44e07d1ba7fab7a41d9b7e567b76929b' NOW (CHAIN 2).
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## SAMPLING FOR MODEL '44e07d1ba7fab7a41d9b7e567b76929b' NOW (CHAIN 3).
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## SAMPLING FOR MODEL '44e07d1ba7fab7a41d9b7e567b76929b' NOW (CHAIN 4).
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## Chain 4: Elapsed Time: 0.05802 seconds (Warm-up)
## Chain 4: 0.061737 seconds (Sampling)
## Chain 4: 0.119757 seconds (Total)
## Chain 4:morph_sq <- brm(culmen_mm~poly(tarsus_mm, 2),
data=morphology,
family= gaussian(link="identity"))## Compiling Stan program...## recompiling to avoid crashing R session## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 2.5e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.25 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1:
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## Chain 1:
## Chain 1: Elapsed Time: 0.045202 seconds (Warm-up)
## Chain 1: 0.03294 seconds (Sampling)
## Chain 1: 0.078142 seconds (Total)
## Chain 1:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 2).
## Chain 2:
## Chain 2: Gradient evaluation took 1.1e-05 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.
## Chain 2: Adjust your expectations accordingly!
## Chain 2:
## Chain 2:
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## Chain 2:
## Chain 2: Elapsed Time: 0.046675 seconds (Warm-up)
## Chain 2: 0.036237 seconds (Sampling)
## Chain 2: 0.082912 seconds (Total)
## Chain 2:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 3).
## Chain 3:
## Chain 3: Gradient evaluation took 1.1e-05 seconds
## Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.
## Chain 3: Adjust your expectations accordingly!
## Chain 3:
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## Chain 3:
## Chain 3: Elapsed Time: 0.046182 seconds (Warm-up)
## Chain 3: 0.034218 seconds (Sampling)
## Chain 3: 0.0804 seconds (Total)
## Chain 3:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 4).
## Chain 4:
## Chain 4: Gradient evaluation took 1.6e-05 seconds
## Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.16 seconds.
## Chain 4: Adjust your expectations accordingly!
## Chain 4:
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## Chain 4:
## Chain 4: Elapsed Time: 0.042654 seconds (Warm-up)
## Chain 4: 0.034908 seconds (Sampling)
## Chain 4: 0.077562 seconds (Total)
## Chain 4:morph_cub <- brm(culmen_mm~poly(tarsus_mm, 3),
data=morphology,
family= gaussian(link="identity"))## Compiling Stan program...## recompiling to avoid crashing R session## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 2.8e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.28 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1:
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## Chain 1:
## Chain 1: Elapsed Time: 0.077607 seconds (Warm-up)
## Chain 1: 0.03647 seconds (Sampling)
## Chain 1: 0.114077 seconds (Total)
## Chain 1:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 2).
## Chain 2:
## Chain 2: Gradient evaluation took 9e-06 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.09 seconds.
## Chain 2: Adjust your expectations accordingly!
## Chain 2:
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## Chain 2:
## Chain 2: Elapsed Time: 0.064797 seconds (Warm-up)
## Chain 2: 0.035297 seconds (Sampling)
## Chain 2: 0.100094 seconds (Total)
## Chain 2:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 3).
## Chain 3:
## Chain 3: Gradient evaluation took 1.3e-05 seconds
## Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.13 seconds.
## Chain 3: Adjust your expectations accordingly!
## Chain 3:
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## Chain 3:
## Chain 3: Elapsed Time: 0.076486 seconds (Warm-up)
## Chain 3: 0.044912 seconds (Sampling)
## Chain 3: 0.121398 seconds (Total)
## Chain 3:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 4).
## Chain 4:
## Chain 4: Gradient evaluation took 1.2e-05 seconds
## Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.12 seconds.
## Chain 4: Adjust your expectations accordingly!
## Chain 4:
## Chain 4:
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## Chain 4:
## Chain 4: Elapsed Time: 0.061962 seconds (Warm-up)
## Chain 4: 0.036221 seconds (Sampling)
## Chain 4: 0.098183 seconds (Total)
## Chain 4:morph_four <- brm(culmen_mm~poly(tarsus_mm, 4),
data=morphology,
family= gaussian(link="identity"))## Compiling Stan program...## recompiling to avoid crashing R session## Trying to compile a simple C file## Running /Library/Frameworks/R.framework/Resources/bin/R CMD SHLIB foo.c
## clang -I"/Library/Frameworks/R.framework/Resources/include" -DNDEBUG -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/Rcpp/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/unsupported" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/BH/include" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/src/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppParallel/include/" -I"/Library/Frameworks/R.framework/Versions/4.0/Resources/library/rstan/include" -DEIGEN_NO_DEBUG -DBOOST_DISABLE_ASSERTS -DBOOST_PENDING_INTEGER_LOG2_HPP -DSTAN_THREADS -DBOOST_NO_AUTO_PTR -include '/Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp' -D_REENTRANT -DRCPP_PARALLEL_USE_TBB=1 -I/usr/local/include -fPIC -Wall -g -O2 -c foo.c -o foo.o
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:88:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:1: error: unknown type name 'namespace'
## namespace Eigen {
## ^
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/src/Core/util/Macros.h:613:16: error: expected ';' after top level declarator
## namespace Eigen {
## ^
## ;
## In file included from <built-in>:1:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/StanHeaders/include/stan/math/prim/mat/fun/Eigen.hpp:13:
## In file included from /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Dense:1:
## /Library/Frameworks/R.framework/Versions/4.0/Resources/library/RcppEigen/include/Eigen/Core:96:10: fatal error: 'complex' file not found
## #include <complex>
## ^~~~~~~~~
## 3 errors generated.
## make: *** [foo.o] Error 1## Start sampling##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 1).
## Chain 1:
## Chain 1: Gradient evaluation took 2.6e-05 seconds
## Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.26 seconds.
## Chain 1: Adjust your expectations accordingly!
## Chain 1:
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## Chain 1:
## Chain 1: Elapsed Time: 0.074392 seconds (Warm-up)
## Chain 1: 0.034481 seconds (Sampling)
## Chain 1: 0.108873 seconds (Total)
## Chain 1:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 2).
## Chain 2:
## Chain 2: Gradient evaluation took 1.1e-05 seconds
## Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 0.11 seconds.
## Chain 2: Adjust your expectations accordingly!
## Chain 2:
## Chain 2:
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## Chain 2:
## Chain 2: Elapsed Time: 0.0806 seconds (Warm-up)
## Chain 2: 0.036416 seconds (Sampling)
## Chain 2: 0.117016 seconds (Total)
## Chain 2:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 3).
## Chain 3:
## Chain 3: Gradient evaluation took 1.5e-05 seconds
## Chain 3: 1000 transitions using 10 leapfrog steps per transition would take 0.15 seconds.
## Chain 3: Adjust your expectations accordingly!
## Chain 3:
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## Chain 3:
## Chain 3: Elapsed Time: 0.087425 seconds (Warm-up)
## Chain 3: 0.03494 seconds (Sampling)
## Chain 3: 0.122365 seconds (Total)
## Chain 3:
##
## SAMPLING FOR MODEL 'e754aa52dd0feb2be6d67820a7a0fe08' NOW (CHAIN 4).
## Chain 4:
## Chain 4: Gradient evaluation took 2.4e-05 seconds
## Chain 4: 1000 transitions using 10 leapfrog steps per transition would take 0.24 seconds.
## Chain 4: Adjust your expectations accordingly!
## Chain 4:
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## Chain 4:
## Chain 4: Elapsed Time: 0.075569 seconds (Warm-up)
## Chain 4: 0.039509 seconds (Sampling)
## Chain 4: 0.115078 seconds (Total)
## Chain 4:#KFOLD####
#all our kfolds with diff poly
morph_k <- kfold(morph_lm, k = 10) ## Fitting model 1 out of 10## Fitting model 2 out of 10## Fitting model 3 out of 10## Fitting model 4 out of 10## Fitting model 5 out of 10## Fitting model 6 out of 10## Fitting model 7 out of 10## Fitting model 8 out of 10## Fitting model 9 out of 10## Fitting model 10 out of 10## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".morph_k##
## Based on 10-fold cross-validation
##
## Estimate SE
## elpd_kfold -1252.8 21.8
## p_kfold 3.2 0.6
## kfoldic 2505.7 43.7morph_k_int <- kfold(morph_int, k = 10) ## Fitting model 1 out of 10## Fitting model 2 out of 10## Fitting model 3 out of 10## Fitting model 4 out of 10## Fitting model 5 out of 10## Fitting model 6 out of 10## Fitting model 7 out of 10## Fitting model 8 out of 10## Fitting model 9 out of 10## Fitting model 10 out of 10## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".morph_k_int##
## Based on 10-fold cross-validation
##
## Estimate SE
## elpd_kfold -1877.0 13.4
## p_kfold 1.4 0.4
## kfoldic 3754.0 26.9morph_k_sq <- kfold(morph_sq, k = 10) ## Fitting model 1 out of 10## Fitting model 2 out of 10## Fitting model 3 out of 10## Fitting model 4 out of 10## Fitting model 5 out of 10## Fitting model 6 out of 10## Fitting model 7 out of 10## Fitting model 8 out of 10## Fitting model 9 out of 10## Fitting model 10 out of 10## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".morph_k_sq##
## Based on 10-fold cross-validation
##
## Estimate SE
## elpd_kfold -1255.6 22.0
## p_kfold 6.2 1.0
## kfoldic 2511.2 44.1morph_k_cub <- kfold(morph_cub, k = 10) ## Fitting model 1 out of 10## Fitting model 2 out of 10## Fitting model 3 out of 10## Fitting model 4 out of 10## Fitting model 5 out of 10## Fitting model 6 out of 10## Fitting model 7 out of 10## Fitting model 8 out of 10## Fitting model 9 out of 10## Fitting model 10 out of 10## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".morph_k_cub##
## Based on 10-fold cross-validation
##
## Estimate SE
## elpd_kfold -1240.6 22.0
## p_kfold 4.5 0.7
## kfoldic 2481.2 44.0morph_k_four <- kfold(morph_four, k = 10) ## Fitting model 1 out of 10## Fitting model 2 out of 10## Fitting model 3 out of 10## Fitting model 4 out of 10## Fitting model 5 out of 10## Fitting model 6 out of 10## Fitting model 7 out of 10## Fitting model 8 out of 10## Fitting model 9 out of 10## Fitting model 10 out of 10## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".## Start sampling## Warning: UNRELIABLE VALUE: Future ('<none>') unexpectedly generated random
## numbers without specifying argument '[future.]seed'. There is a risk that those
## random numbers are not statistically sound and the overall results might be
## invalid. To fix this, specify argument '[future.]seed', e.g. 'seed=TRUE'. This
## ensures that proper, parallel-safe random numbers are produced via the L'Ecuyer-
## CMRG method. To disable this check, use [future].seed=NULL, or set option
## 'future.rng.onMisuse' to "ignore".morph_k_four##
## Based on 10-fold cross-validation
##
## Estimate SE
## elpd_kfold -1243.0 22.0
## p_kfold 6.8 0.9
## kfoldic 2486.1 44.0#compare kfolds
loo_compare(morph_k_four,morph_k_cub, morph_k_sq, morph_k_int, morph_k)## elpd_diff se_diff
## morph_cub 0.0 0.0
## morph_four -2.4 1.0
## morph_lm -12.3 5.2
## morph_sq -15.0 5.7
## morph_int -636.4 23.8#LOO####
#loo of our poly's
morph_loo <- loo(morph_lm)
morph_loo##
## Computed from 4000 by 766 log-likelihood matrix
##
## Estimate SE
## elpd_loo -1252.8 21.9
## p_loo 3.1 0.3
## looic 2505.6 43.7
## ------
## Monte Carlo SE of elpd_loo is 0.0.
##
## All Pareto k estimates are good (k < 0.5).
## See help('pareto-k-diagnostic') for details.morph_loo_int <- loo(morph_int)
morph_loo_int##
## Computed from 4000 by 766 log-likelihood matrix
##
## Estimate SE
## elpd_loo -1877.1 13.5
## p_loo 1.5 0.1
## looic 3754.1 26.9
## ------
## Monte Carlo SE of elpd_loo is 0.0.
##
## All Pareto k estimates are good (k < 0.5).
## See help('pareto-k-diagnostic') for details.morph_loo_sq <- loo(morph_sq)
morph_loo_sq##
## Computed from 4000 by 766 log-likelihood matrix
##
## Estimate SE
## elpd_loo -1254.0 21.9
## p_loo 4.6 0.7
## looic 2508.0 43.9
## ------
## Monte Carlo SE of elpd_loo is 0.0.
##
## All Pareto k estimates are good (k < 0.5).
## See help('pareto-k-diagnostic') for details.morph_loo_cub <- loo(morph_cub)
morph_loo_cub##
## Computed from 4000 by 766 log-likelihood matrix
##
## Estimate SE
## elpd_loo -1240.5 22.1
## p_loo 4.4 0.4
## looic 2481.0 44.1
## ------
## Monte Carlo SE of elpd_loo is 0.0.
##
## All Pareto k estimates are good (k < 0.5).
## See help('pareto-k-diagnostic') for details.morph_loo_four <- loo(morph_four)
morph_loo_four##
## Computed from 4000 by 766 log-likelihood matrix
##
## Estimate SE
## elpd_loo -1241.4 22.0
## p_loo 5.2 0.5
## looic 2482.8 44.0
## ------
## Monte Carlo SE of elpd_loo is 0.0.
##
## All Pareto k estimates are good (k < 0.5).
## See help('pareto-k-diagnostic') for details.#compare loos
loo_compare(morph_loo, morph_loo_int,morph_loo_sq,morph_loo_cub,morph_loo_four)## elpd_diff se_diff
## morph_cub 0.0 0.0
## morph_four -0.9 0.3
## morph_lm -12.3 5.3
## morph_sq -13.5 5.6
## morph_int -636.5 23.8